travel time and distance formula

Module 9: Multi-Step Linear Equations

Using the distance, rate, and time formula, learning outcomes.

• Use the problem-solving method to solve problems using the distance, rate, and time formula

One formula you’ll use often in algebra and in everyday life is the formula for distance traveled by an object moving at a constant speed. The basic idea is probably already familiar to you. Do you know what distance you traveled if you drove at a steady rate of [latex]60[/latex] miles per hour for [latex]2[/latex] hours? (This might happen if you use your car’s cruise control while driving on the Interstate.) If you said [latex]120[/latex] miles, you already know how to use this formula!

The math to calculate the distance might look like this:

[latex]\begin{array}{}\\ \text{distance}=\left(\Large\frac{60\text{ miles}}{1\text{ hour}}\normalsize\right)\left(2\text{ hours}\right)\hfill \\ \text{distance}=120\text{ miles}\hfill \end{array}[/latex]

In general, the formula relating distance, rate, and time is

[latex]\text{distance}\text{=}\text{rate}\cdot \text{time}[/latex]

Distance, Rate, and Time

For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula

[latex]d=rt[/latex]

where [latex]d=[/latex] distance, [latex]r=[/latex] rate, and [latex]t=[/latex] time.

Notice that the units we used above for the rate were miles per hour, which we can write as a ratio [latex]\Large\frac{miles}{hour}[/latex]. Then when we multiplied by the time, in hours, the common units “hour” divided out. The answer was in miles.

Jamal rides his bike at a uniform rate of [latex]12[/latex] miles per hour for [latex]3\Large\frac{1}{2}[/latex] hours. How much distance has he traveled?

In the following video we provide another example of how to solve for distance given rate and time.

Rey is planning to drive from his house in San Diego to visit his grandmother in Sacramento, a distance of [latex]520[/latex] miles. If he can drive at a steady rate of [latex]65[/latex] miles per hour, how many hours will the trip take?

Show Solution

In the following video we show another example of how to find rate given distance and time.

• Question ID 145550, 145553,145619,145620. Authored by : Lumen Learning. License : CC BY: Attribution
• Ex: Find the Rate Given Distance and Time. Authored by : James Sousa (Mathispower4u.com). Located at : https://youtu.be/3rYh32ErDaE . License : CC BY: Attribution
• Example: Solve a Problem using Distance = Rate x Time. Authored by : James Sousa (Mathispower4u.com). Located at : https://youtu.be/lMO1L_CvH4Y . License : CC BY: Attribution
• Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

Speed Distance Time Calculator

Please enter the speed and distance values to calculate the travel time in hours, minutes and seconds.

About Speed Distance Time Calculator

This online calculator tool can be a great help for calculating time basing on such physical concepts as speed and distance. Therefore, in order to calculate the time, both distance and speed parameters must be entered. For the speed , you need to enter its value and select speed unit by using the scroll down menu in the calculator. For distance , you should enter its value and also select the proper length measurement unit from the scroll down menu. You'll receive the result in standard time format (HH:MM:SS).

Time Speed Distance Formula

Distance is equal to speed × time. Time is equal Distance/Speed.

Calculate Time from Distance and Speed Examples

Recent comments.

One of the best tools I've found for the calculations.

Going 65mph for 30 seconds how far would you get? None of these formulas work without distance. How would I find the distance from time and speed?

if i travel 0.01 inches per second and I need to travel 999999999 kilometers, it takes 556722071 Days and 20:24:34 WHAT

4. How long does it take to do 100m at 3kph ? No I thought you would just divide 100 ÷ 3 = which 33.33333 so 33 seconds or so I thought. But apparently it 2 mins.

This was the best tool ive ever used that was on point from speed to distance and time Calculator

This was somewhat unhelpful as I know the time and distance, but not the speed. Would be helpful if this calculator also could solve the other two as well.

If a total distance of 2 miles is driven, with the first mile being driven at a speed of 15mph, and the second mile driven at a speed of 45 mph: What is the average speed of the full 2 mile trip?

hi sorry im newly introduced to this and i dont understand how to use it but in need to find the distance if i was travelling in the average speed of 15km/hr in 4 hours how far would i travel

D= 697 km T= 8 hours and 12 minutes S= ?

if a train is going 130 miles in 50 minutes, how fast is it going in miles per hour ??

whats the speed if you travel 2000 miles in 20hours?

How long would it take me to drive to Mars at 100 miles per hour and how much gas would I use in a 2000 Ford Mustang000000/ Also, how much CO2 would I release into the air?

great tool helped me alot

A car can go from rest to 45 km/hr in 5 seconds. What is its acceleration?

Guys how much time will a cyclist take to cover 132 METRES With a speed of 8 km/ph

@Mike Depends on how fast that actually is. For every 10 mph above 60, but below 120, you save 5 seconds a mile. But between the 30-60 area, every ten saves 10 seconds a mile (if I am remembering correctly), and every 10 between 15-30 is 20 seconds. Realistically, it isn't likely isn't worth it, unless it is a relatively straight drive with no stops, in which case you will likely go up a gear for the drive and thus improve gas efficiency for the trip. Only really saves time if it is over long trips 300+ miles (in which case, assuming you were on the interstate) that 5 seconds a mile would save you 25 minutes from the drive, making it go from 4h35m to 4h10m. For me, I have family across the U.S., so family visits are usually 900-1400 miles. Even only driving 5 above usually saves me 90-150 minutes or so (since I often have stretches where I drive on US highways which have 55 mph speed limits)

I would like to know if driving fast is worth it for short trips. If I drive 10 MPH over the speed limit for 10 miles, how much time do i save ? Is there an equation for that ?

it helps me in lot of stuff

awesome, helped me notice how long my taiga (electric seedoo) is going to last.

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Speed, Distance, and Time

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Classical mechanics.

Hardcore training for the aspiring physicist.

A common set of physics problems ask students to determine either the speed, distance, or travel time of something given the other two variables. These problems are interesting since they describe very basic situations that occur regularly for many people. For example, a problem might say: "Find the distance a car has traveled in fifteen minutes if it travels at a constant speed of \(75 \text {km/hr}\)." Often in these problems, we work with an average velocity or speed, which simplifies the laws of motion used to calculate the desired quantity. Let's see how that works.

Application and Extensions

As long as the speed is constant or average, the relationship between speed , distance , and time is expressed in this equation

\[\mbox{Speed} = \frac{\mbox{Distance}}{\mbox{Time}},\]

which can also be rearranged as

\[\mbox{Time} = \frac{\mbox{Distance}}{\mbox{Speed}}\]

\[\mbox{Distance} = \mbox{Speed} \times \mbox{Time}.\]

Speed, distance, and time problems ask to solve for one of the three variables given certain information. In these problems, objects are moving at either constant speeds or average speeds.

Most problems will give values for two variables and ask for the third.

Bernie boards a train at 1:00 PM and gets off at 5:00 PM. During this trip, the train traveled 360 kilometers. What was the train's average speed in kilometers per hour? In this problem, the total time is 4 hours and the total distance is \(360\text{ km},\) which we can plug into the equation: \[\mbox{Speed} = \frac{\mbox{Distance}}{\mbox{Time}}= \frac{360~\mbox{km}}{4~\mbox{h}} = 90~\mbox{km/h}. \ _\square \]

When working with these problems, always pay attention to the units for speed, distance, and time. Converting units may be necessary to obtaining a correct answer.

A horse is trotting along at a constant speed of 8 miles per hour. How many miles will it travel in 45 minutes? The equation for calculating distance is \[\mbox{Distance} = \mbox{Speed} \times \mbox{Time},\] but we won't arrive at the correct answer if we just multiply 8 and 45 together, as the answer would be in units of \(\mbox{miles} \times \mbox{minute} / \mbox{hour}\). To fix this, we incorporate a unit conversion: \[\mbox{Distance} = \frac{8~\mbox{miles}}{~\mbox{hour}} \times 45~\mbox{minutes} \times \frac{1~\mbox{hour}}{60~\mbox{minutes}} = 6~\mbox{miles}. \ _\square \] Alternatively, we can convert the speed to units of miles per minute and calculate for distance: \[\mbox{Distance} = \frac{2}{15}~\frac{\mbox{miles}}{\mbox{minute}} \times 45~\mbox{minutes} = 6~\mbox{miles},\] or we can convert time to units of hours before calculating: \[\mbox{Distance} = 8~\frac{\mbox{miles}}{\mbox{hour}} \times \frac{3}{4}~\mbox{hours} = 6~\mbox{miles}.\] Any of these methods will give the correct units and answer. \(_\square\)

In more involved problems, it is convenient to use variables such as \(v\), \(d\), and \(t\) for speed, distance, and velocity, respectively.

Alice, Bob, Carly, and Dave are in a flying race!

Alice's plane is twice as fast as Bob's plane. When Alice finishes the race, the distance between her and Carly is \(D.\) When Bob finishes the race, the distance between him and Dave is \(D.\)

If Bob's plane is three times as fast as Carly's plane, then how many times faster is Alice's plane than Dave's plane?

Albert and Danny are running in a long-distance race. Albert runs at 6 miles per hour while Danny runs at 5 miles per hour. You may assume they run at a constant speed throughout the race. When Danny reaches the 25 mile mark, Albert is exactly 40 minutes away from finishing. What is the race's distance in miles? \[\] Let's begin by calculating how long it takes for Danny to run 25 miles: \[\mbox{Time} = \frac{\mbox{Distance}}{\mbox{Speed}}= \frac{25~\mbox{miles}}{5~\mbox{miles/hour}}= 5~\mbox{hours}.\] So, it will take Albert \(5~\mbox{hours} + 40~\mbox{minutes}\), or \(\frac{17}{3}~\mbox{hours}\), to finish the race. Now we can calculate the race's distance: \[\begin{align} \mbox{Distance} &= \mbox{Speed} \times \mbox{Time} \\ &= (6~\mbox{miles/hour}) \times \left(\frac{17}{3}~\mbox{hours}\right) \\ &= 34~\mbox{miles}.\ _\square \end{align}\]

A cheetah spots a gazelle \(300\text{ m}\) away and sprints towards it at \(100\text{ km/h}.\) At the same time, the gazelle runs away from the cheetah at \(80\text{ km/h}.\) How many seconds does it take for the cheetah to catch the gazelle? \[\] Let's set up equations representing the distance the cheetah travels and the distance the gazelle travels. If we set distance \(d\) equal to \(0\) as the cheetah's starting point, we have \[\begin{align} d_\text{cheetah} &= 100t \\ d_\text{gazelle} &= 0.3 + 80t. \end{align}\] Note that time \(t\) here is in units of hours, and \(300\text{ m}\) was converted to \(0.3\text{ km}.\) The cheetah catches the gazelle when \[\begin{align} d_\text{cheetah} &=d_\text{gazelle} \\ 100t &= 0.3 + 80t \\ 20t &= 0.3 \\ t &= 0.015~\mbox{hours}. \end{align}\] Converting that answer to seconds, we find that the cheetah catches the gazelle in \(54~\mbox{seconds}\). \(_\square\)

Two friends are crossing a hundred meter railroad bridge when they suddenly hear a train whistle. Desperate, each friend starts running, one towards the train and one away from the train. The one that ran towards the train gets to safety just before the train passes, and so does the one that ran in the same direction as the train.

If the train is five times faster than each friend, then what is the train-to-friends distance when the train whistled (in meters)?

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Speed Distance Time Calculator

Initially, this amazing calculator was developed especially for athletes, cyclists or joggers. However, all people who are required due to their activities to calculate an unknown variable with the help of the other two variables, will find use in it. You can use it in two ways. First, enter two particular variables in order to find the third one. Second, you may find the variable by entering the details.

Time can be entered as hh:mm:ss , mm:ss or ss (hh=hours mm=minutes ss=seconds).

Example Time Formats:

• 1:20:45 = 1 hour, 20 minutes and 45 seconds
• 18:25 = 18 minutes and 25 seconds
• 198 = 198 seconds = 3 minutes and 18 seconds

Speed: miles yards feet inches kilometers meters centimeters per hour minute second

Distance: miles yards feet inches kilometers meters centimeters millimeters

You may set the number of decimal places in the online calculator. By default there are only two decimal places.

0 1 2 3 4 5 6 7 8 9 Decimal Places

Speed    miles/hr miles/min miles/sec yards/hr yards/min yards/sec feet/hr feet/min feet/sec inch/hr inch/min inch/sec km/hr km/min km/sec meter/hr meter/min meter/sec cm/hr cm/min cm/sec mm/hr mm/min mm/sec

Distance    miles yards feet inches kilometers meters centimeters millimeters

Time (hh:mm:ss)

This calculator includes the following algorithms:

Speed = Distance divided by Time

Distance = Speed multiplied by Time

Time = Distance divided by Speed

You may also be interested in our Running Pace Calculator or Steps to Miles Calculator

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Savvy Calculator

Savvy Calculator is a free online tool of calculations.

Distance Speed Time Calculator

Introduction.

In the world of physics and motion, understanding the relationships between distance, speed, and time is crucial. Whether you’re a student working on a physics problem or a traveler planning a journey, the Distance Speed Time (DST) Calculator can be a valuable tool. This calculator allows you to easily determine one of the three variables when the other two are known, providing a convenient way to analyze and plan various activities.

The basic formula relating distance, speed, and time is:

Distance=Speed×Time Distance = Speed × Time

This formula serves as the foundation for the Distance Speed Time Calculator. By rearranging the equation, you can also find the speed or time:

Speed=DistanceTime Speed = Time Distance ​

Time=DistanceSpeed Time = Speed Distance ​

These formulas offer flexibility in solving real-world problems, making the calculator a versatile tool for a wide range of applications.

How to Use?

Using the Distance Speed Time Calculator is straightforward. Simply input the values you know, such as distance, speed, or time, into the appropriate fields. The calculator will then automatically compute the missing variable based on the provided information. Whether you’re a student solving physics problems or a traveler planning a road trip, this tool can save time and ensure accurate calculations.

Let’s consider an example to illustrate the practical use of the Distance Speed Time Calculator:

Suppose you are planning a road trip and need to cover a distance of 300 miles. You want to know how long it will take if you travel at an average speed of 60 miles per hour.

• Input the distance: 300 miles
• Input the speed: 60 miles per hour
• Leave the time field blank

The calculator will then compute the time it takes to cover the specified distance at the given speed.

Q1: Can the Distance Speed Time Calculator be used for any units of measurement?

A1: Yes, the calculator is unit-agnostic. You can use any consistent units for distance, speed, and time, such as miles, kilometers, miles per hour, or meters per second.

Q2: Is the calculator applicable only to linear motion?

A2: While the basic formula assumes constant speed, the calculator can still provide useful estimates for scenarios involving variable speeds by using average values.

Q3: How accurate are the calculations?

A3: The calculator provides accurate results based on the input values. However, it’s essential to consider factors like acceleration, deceleration, and changes in speed for more complex scenarios.

Conclusion:

The Distance Speed Time Calculator is a valuable tool for anyone dealing with motion-related problems. Whether you are a student, a traveler, or someone involved in transportation logistics, this calculator simplifies the process of determining distance, speed, or time. By understanding the fundamental formula and utilizing this user-friendly tool, you can confidently tackle a wide range of real-world scenarios involving motion and travel.

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Speed Calculator

How to calculate speed - average speed formula, solving the speed equation to calculate distance and time, speed vs. velocity.

If you're searching for how to calculate the speed-time-distance relationship, this speed calculator is for you! With this calculator, you can:

• Calculate speed , given distance and time;
• By inputting speed and distance, calculate time ;
• Calculate distance ;
• Compare the time with a different speed, using the advanced mode in the calculator.

Consider that when we use total distance covered and time traveled (as in this calculator), we calculate an average speed . The final section discusses this and the difference between speed and velocity .

CalcTool's internal unit conversion allows you to conveniently have the inputs and outputs in different units. If you have doubts about calculating miles per hour and other velocity units, you can look at our speed converter .

Once you've mastered speed and velocity, you'll be ready to study acceleration with our acceleration calculator .

Speed is equal to the distance traveled divided by the time taken:

speed = distance/time

It's important to know that this is an average speed formula , as going over some distance in a specific amount of time could be done at different speeds during that travel.

Now that you know how to find the speed let's see how to calculate distance and time.

If we know the average speed and time, we can solve the previous speed equation for distance :

distance = speed × time

And do the same for time :

time = distance/speed

Speed and velocity might seem the same, but they're not.

• Speed is a scalar quantity - it has magnitude only but not direction. In simple terms, it tells how fast an object moves.
• Velocity is a vector quantity - it is defined not only by magnitude but also by direction . It tells the rate at which an object changes its position.

While speed depends on distance traveled, velocity depends on initial and final positions . If the initial and final positions are the same, the position doesn't change, and the average velocity equals zero.

Suppose a car travels from point A to point B and returns to point A, all that in 30 seconds. If there's a distance of 50 m between both points, the car had an average speed of:

speed = distance/time = (2 × 50 m)/30 s = 3.33 m/s

On the other hand, the velocity is zero, as the initial and final positions are the same.

Ground speed

Horizontal projectile motion, schwarzschild radius.

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How to Calculate Speed, Distance & Time

Working out speed, distance and time is an important part of many roles, including those in the armed forces or transport industries.

If you are applying for a role in these industries, you may be tested on this as part of your recruitment process. The questions will allow your employer to test your applied mathematical abilities.

How to calculate speed, distance & time: the formula triangle you’ll need?

To work out speed, divide the distance of the journey by the time it took to travel, so speed = distance divided by time. To calculate time, divide the distance by speed. To get the distance, multiply the speed by time.

You may see these equations simplified as s=d/t, where s is speed, d is distance, and t is time.

This formula can be arranged into the triangle above. In the triangle, speed and time form the base, as they are what is multiplied together to work out the distance.

The triangle is an easy way to remember the formula and can save you time when working out your exam questions. The triangle will help you remember the three formulas:

• The formula of speed is Speed = Distance ÷ Time
• The formula of time is Time = Distance ÷ Speed
• The formula of distance is Distance = Speed x Time

The triangle shows you what calculation you should use. As distance is at the top of the triangle, to work it out, you need to multiply speed with time.

As speed and time are at the bottom of the triangle, you need to divide this number from the figure for distance, to work out the correct answer.

When beginning to study for your practice test, make sure you write out the triangle on your paper. This will help you to memorize it.

How to calculate speed

To calculate speed, you need to divide the distance by the time. You can work this out by using the triangle. If you cover up speed, you are left with distance over time.

Here is an example:

If a driver has travelled 180 miles and it took them 3 hours to make that distance, then to work out their speed you would take:

180 miles / 3 hours -\> 180 / 3 = 60

So the driver’s speed would be 60mph.

How to calculate distance

To work out the distance travelled, you will need to multiply speed and time.

If a driver travelled at 100mph for 4 hours, then to work out the distance you will need to multiply the speed with the time.

100mph x 4 hours -\> 100 x 4 = 400

The distance is 400 miles.

How to calculate the time

To work out the time that the journey took, you will need to know the speed of the journey and the distance that was travelled.

If the driver travelled 50 miles at 5mph, then to work out the time taken you would divide:

50miles / 5 miles per hour -\> 50 / 5 = 10

The time taken to travel this distance is 10 miles per hour.

Three example speed/distance/time questions

• Andy drives his lorry for 400 miles, which takes him 8 hours. Harry drives 200 miles, which takes him 4.5 hours. Who is travelling faster?

Answer: Andy is driving at 50mph, and Harry is driving at 44.44mph. So, Andy is driving faster.

• Tessa runs a 5km race with her running club every Saturday. She runs this in 40 minutes. If she maintains the same speed, how long would it take her to run the 8km race?

Answer: Her speed is 7.5kph. If she runs 10km at 7.5kph, to work out the time, you need to divide 8 by 7.5, which equals 1.066. If we convert this into hours and minutes, it will take her 1 hour and 4 minutes to run 8km.

• Hannah goes on a cycling trip. In the first half of the journey, she travels at 10mph for 2 hours. In the second half, she travels at 20mph for 90 minutes. How far does she travel in total?

Answer: In the first half of her journey she travels 20 miles (10 x 2 = 20). In the second half, she travels 30 miles, (20 x 1.5 = 30). 20+30 =50, so she travels 50 miles in total.

Methods to get better at these questions

To improve your skill in answering speed distance time questions, there are two main things you can do.

First, make sure that you are familiar with the formula triangle. The key to answering these questions is knowing the formula inside out, so that you always know what equation to use, whether the exam question is asking you to work out speed or distance.

By making sure you have memorized the formula in all its variations, you will save yourself time when answering questions.

Secondly, you should focus on improving your general mathematical skills. You may get a compound question, which asks you to use the formula in conjunction with other maths skills to work out the answer to the problem.

You can try a few maths practice tests, such as these , which will help you to practise your basic numeracy skills.

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Distance Speed Time Formula

Speed is a measure of how quickly an object moves from one place to another. It is equal to the distance traveled divided by the time. It is possible to find any of these three values using the other two. This picture is helpful:

The positions of the words in the triangle show where they need to go in the equations. To find the speed, distance is over time in the triangle, so speed is distance divided by time. To find distance, speed is beside time, so distance is speed multiplied by time.

s = speed (meters/second)

d = distance traveled (meters)

t = time (seconds)

1) A dog runs from one side of a park to the other. The park is 80.0 meters across. The dog takes 16.0 seconds to cross the park. What is the speed of the dog?

Answer: The distance the dog travels and the time it takes are given. The dog’s speed can be found with the formula:

s = 5.0 m/s

The speed of the dog is 5.0 meters per second.

2) A golf cart is driven at its top speed of 27.0 km/h for 10.0 minutes. In meters, how far did the golf cart travel?

Answer: The first step to solve this problem is to change the units of the speed and time so that the answer found will be in meters, since this is what the question asks for. The speed is:

s = 27.0 km/h

s = 7.50 m/s

Converting the units, the speed is 7.50 m/s. The time the cart traveled for was:

t = 10.0 min

d = (7.50 m/s)(600 s)

The golf cart traveled 4500 m, which is equal to 4.50 km.

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Distance and Average Speed to Travel Time Calculator

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✕ clear settings

Flip tool with current settings and calculate average speed or total distance

Related Tools

• Average speed calculator
• Travel distance calculator
• Convert speed into different units
• Convert distance into different units
• Convert time duration into different units

This calculator will estimate the travel time for a journey using the travel distance to destination and the expected average speed of the method of travel.

Once a distance and speed have been entered the calculated time will be displayed in the answer box. Also a conversion scale will be generated for different values of distance versus time at the same speed.

This tool estimates the journey time with the following formula:

• d = Distance

Distance Travelled

Enter the expected distance to be travelled in any units.

Average Speed

Enter the estimated average speed of the intended method of transport.

Time Estimate

This is an estimate of the total time it will take to complete the journey without any delays.

• Physics Formulas

Distance Speed Time Formula

Speed Distance Time Formula

Speed is the rate at which an object moves. It’s a very basic concept in motion and all about how fast or slow an object can move. Speed is simply distance divided by the time where distance is directly proportional to velocity when time is constant. Problems related to speed, distance, and time, will ask you to calculate for one of three variables given.

The formula for speed distance time is mathematically given as:

Speed = Distance/Time

x = Speed in m/s,

d = Distance travelled in m,

t= time taken in s.

Distance travelled formula

If any of the two values among speed , distance and time are given, we can use this formula and find the unknown quantity.

Solved Examples

Question 1 : Lilly is driving a scooter with a speed of 6 km/hr for 2hr. Calculate the distance travelled by her?

Speed of the scooter x = 6km/hr

Time taken, t = 2 hr

Distance travelled d = ?

Speed distance time formula is given as

Distance travelled d = x × t

                            = 6 km/hr × 2 hr

                            = 12 km.

Question 2 : A man has covered a distance of 80 miles in 4 hours. Calculate the speed of the bike?

Given: Distance Covered d = 80 miles,

Time taken, t = 4 hours

Speed is calculated using the formula: x = d/t

                                                           = 80/4

                                                           = 20 miles/hr.

Question 3 : In a cycle race, a cyclist is moving with a speed of 2 km/hr. He has to cover a distance of 5 km. Calculate the time will he need to reach his destiny?

Given: Speed x = 2 km/hr,

Distance Covered d = 5 km,

time taken t = ?

Speed is given by formula: x = d/t

Time taken t = d/x

                   = 5 km/2 km/hr

                   = 2.5 hrs

Time taken by the Cyclist = 2.5 hrs

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Solving Problems Involving Distance, Rate, and Time

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In math, distance, rate, and time are three important concepts you can use to solve many problems if you know the formula. Distance is the length of space traveled by a moving object or the length measured between two points. It is usually denoted by d in math problems .

The rate is the speed at which an object or person travels. It is usually denoted by  r  in equations . Time is the measured or measurable period during which an action, process, or condition exists or continues. In distance, rate, and time problems, time is measured as the fraction in which a particular distance is traveled. Time is usually denoted by t in equations. 

Solving for Distance, Rate, or Time

When you are solving problems for distance, rate, and time, you will find it helpful to use diagrams or charts to organize the information and help you solve the problem. You will also apply the formula that solves distance, rate, and time, which is  distance = rate x tim e. It is abbreviated as:

There are many examples where you might use this formula in real life. For example, if you know the time and rate a person is traveling on a train, you can quickly calculate how far he traveled. And if you know the time and distance a passenger traveled on a plane, you could quickly figure the distance she traveled simply by reconfiguring the formula.

Distance, Rate, and Time Example

You'll usually encounter a distance, rate, and time question as a word problem in mathematics. Once you read the problem, simply plug the numbers into the formula.

For example, suppose a train leaves Deb's house and travels at 50 mph. Two hours later, another train leaves from Deb's house on the track beside or parallel to the first train but it travels at 100 mph. How far away from Deb's house will the faster train pass the other train?

To solve the problem, remember that d represents the distance in miles from Deb's house and t  represents the time that the slower train has been traveling. You may wish to draw a diagram to show what is happening. Organize the information you have in a chart format if you haven't solved these types of problems before. Remember the formula:

distance = rate x time

When identifying the parts of the word problem, distance is typically given in units of miles, meters, kilometers, or inches. Time is in units of seconds, minutes, hours, or years. Rate is distance per time, so its units could be mph, meters per second, or inches per year.

Now you can solve the system of equations:

50t = 100(t - 2) (Multiply both values inside the parentheses by 100.) 50t = 100t - 200 200 = 50t (Divide 200 by 50 to solve for t.) t = 4

Substitute t = 4 into train No. 1

d = 50t = 50(4) = 200

Now you can write your statement. "The faster train will pass the slower train 200 miles from Deb's house."

Sample Problems

Try solving similar problems. Remember to use the formula that supports what you're looking for—distance, rate, or time.

d = rt (multiply) r = d/t (divide) t = d/r (divide)

Practice Question 1

A train left Chicago and traveled toward Dallas. Five hours later another train left for Dallas traveling at 40 mph with a goal of catching up with the first train bound for Dallas. The second train finally caught up with the first train after traveling for three hours. How fast was the train that left first going?

Remember to use a diagram to arrange your information. Then write two equations to solve your problem. Start with the second train, since you know the time and rate it traveled:

Second train t x r = d 3 x 40 = 120 miles First train t x r = d 8 hours x r = 120 miles Divide each side by 8 hours to solve for r. 8 hours/8 hours x r = 120 miles/8 hours r = 15 mph

Practice Question 2

One train left the station and traveled toward its destination at 65 mph. Later, another train left the station traveling in the opposite direction of the first train at 75 mph. After the first train had traveled for 14 hours, it was 1,960 miles apart from the second train. How long did the second train travel? First, consider what you know:

First train r = 65 mph, t = 14 hours, d = 65 x 14 miles Second train r = 75 mph, t = x hours, d = 75x miles

Then use the d = rt formula as follows:

d (of train 1) + d (of train 2) = 1,960 miles 75x + 910 = 1,960 75x = 1,050 x = 14 hours (the time the second train traveled)

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Time, Speed and Distance

Time, speed and distance: formulas, tricks, examples and online test.

Speed: The distance covered per unit time is called speed. Speed is directly proportional to distance and inversely to time

• Speed = Distance/Time;
• Time = Distance/Speed
• Distance = Speed × time
• Time : Seconds, minutes, hours
• Distance : meter, kilometer
• Speed : km/ hr, m /sec

Conversion of Units:

• 1 km/hr = 5/18 metre/second
• 1 metre/second = 18/5 km/hr
• 1 Km/hr = 5/8 mile/hr
• 1 mile/hr = 22/15 foot/second

Example 1: A scooter travels at the speed of 45 kmph. What is the distance covered by the scooter in 4 minutes?

Solution: Speed of scooter = 45 km/hr

∴ Distance covered in 4 minutes = 4 × 750 = 3000 metre

Quicker Method to solve the questions

Average speed.

The average speed is given by total distance divided by total time taken; this is the formula to be remembered all the time. Average Speed =

The average speed in case of a journey from X to Y at speed of A m/sec and returning back to X at a speed of B m/sec, is metre/second

Example 2: Sunil travels from Delhi to Patna at the speed of 40 km/hr and returns at the speed of 50 km/hr, what is the average speed of the journey?

= 44.44 Km/hr

While travelling a certain distance d, if a man changes his speed in the ratio m:n, then the ratio of time taken becomes n:m.

If a body travels a distance ‘d’ from A to B with speed ‘a’ in time t₁ and travels back from B to A i.e., the same distance with m/n of the usual speed ‘a’, then the change in time taken to cover the same distance is given by: Change in time = × t₁; for n > m = × t₁; for m > n If first part of the distance is covered at the rate of v₁ in time t₁ and the second part of the distance is covered at the rate of v₂ in time t₂, then the average speed is

Relative Speed

As the name suggests, the concept is regarding the relative speed between two or more objects. The basic concept in relative speed is that speeds get added in case objects are moving from opposite direction, and get subtracted in case objects are moving in the same direction. For example, if two trains are moving in opposite direction with a speed of X km/hr and Y km/hr respectively, then (X + Y) is their relative speed. In the other case if two trains are moving in the same direction with a speed of X km/hr and Y km/hr respectively, then (X – Y) is their relative speed.

For the first case the time taken by the trains in passing each other = hours, where L₁ and L₂ are length of trains. For the second case the time taken by the trains in passing each other = hours, where L₁ and L₂ are length of trains.

Example 3: Two trains, 100 m and 80 m in length are running in the same direction. The first runs at the rate of 51 m/s and the second at the rate of 42 m/s. How long will they take to cross each other?

Solution: Here Length of first train = 100m,

Length of second train = 80m

And Speed of first train = 51 m/s

Speed of second train = 42 m/s

Relative speed = 51 – 42 = 9 m/s

(since trains are running in the same direction)

As per the formula

Example 4: Two trains, 100 m and 80 m in length are running in opposite direction. The first runs at the rate of 10 m/s and the second at the rate of 15 m/s. How long will they take to cross each other?

Solution: Here Length of first train = 100 m

Length of second train = 80 m

And Speed of first train = 10 m/s

Speed of second train = 15 m/s

Relative speed = 10 + 15 = 25 m/s

(since trains are running in opposite directions)

Example 5: The driver of a maruti car driving at the speed of 68 km/h locates a bus 40 metres ahead of him. After 10 seconds, the bus is 60 metres behind. The speed of the bus is

Solution: (2) Let speed of Bus = SB km/h.

Now, in 10 sec., car covers the relative distance = (60 + 40) m = 100 m

∴ Relative speed of car

If two persons (or vehicles or trains) start at the same time in opposite directions from two points A and B, and after crossing each other they take x and y hours respectively to complete the journey, then

⇒ 2nd train’s speed = 70 km/h.

If new speed is of usual speed, then Usual time

Example 7: A boy walking at 3/5 of his usual speed, reaches his school 14 min late. Find his usual time to reach the school.

Solution: Usual time

The time taken by a train, X metre long to pass a signal post is the time taken for the train to cover X metres.

Example 8: A train 300 meters long has a speed of 10 m/s. How long will it take to pass an electric pole?

The distance here will be same as the length of the train.

That is 300 meters.

The time taken by a x meter long train in passing any object which is y meter long is the time taken for the train to cover the distance x + y.

Example 9: A train 300 meters long has a speed of 10 m/s. How long will it take to pass a platform of 50 meters?

The distance here will be same as the

length of the train + the length of the platform.

This is 300 + 50 = 350 m

A man covers a certain distance D. If he moves S₁ speed faster, he would have taken t time less and if he moves S₂ speed slower, he would have taken t time more. The original speed is given by

Example 10: A man covers a certain distance on scooter. Had he moved 3 km/h faster, he would have taken 20 min less. If he had moved 2 km/h slower, he would have taken 20 min more. Find the original speed.

If a person with two different speeds U & V cover the same distance, then required distance Also, required distance

Example 11: A boy walking at a speed of 10 km/h reaches his school 12 min late. Next time at a speed of 15 km/h reaches his school 7 min late. Find the distance of his school from his house?

Solution: Difference between the time

A man leaves a point A at t₁ and reaches the point B at t₂. Another man leaves the point B at t₃ and reaches the point A at t₄, then they will meet at

Example 12: A bus leaves Ludhiana at 5 am and reaches Delhi at 12 noon. Another bus leaves Delhi at 8 am and reaches Ludhiana at 3 pm. At what time do the buses meet?

Solution: Converting all the times into 24 hour clock time, we get 5 am = 500, 12 noon = 1200, 8 am = 800 and 3 pm = 1500

Relation between time taken with two different modes of transport: t₂x + t₂y = 2(tx + ty)

• tx = time when mode of transport x is used single way.
• ty = time when mode of transport y is used single way.
• t₂x = time when mode of transport x is used both ways.
• t₂y = time when mode of transport y is used both ways.

Solution: (2) Clearly, time taken by him to go by scooter both way

= 6h.30m – 2h.10m

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How to Calculate Distance

Last Updated: April 19, 2024 Fact Checked

This article was reviewed by Grace Imson, MA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. There are 7 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 320,870 times.

Distance, often assigned the variable d , is a measure of the space contained by a straight line between two points. [1] X Research source Distance can refer to the space between two stationary points (for instance, a person's height is the distance from the bottom of his or her feet to the top of his or her head) or can refer to the space between the current position of a moving object and its starting location. Most distance problems can be solved with the equations d = s avg × t where d is distance, s avg is average speed, and t is time, or using d = √((x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 ) , where (x 1 , y 1 ) and (x 2 , y 2 ) are the x and y coordinates of two points.

Finding Distance with Average Speed and Time

• To better understand the process of using the distance formula, let's solve an example problem in this section. Let's say that we're barreling down the road at 120 miles per hour (about 193 km per hour) and we want to know how far we will travel in half an hour. Using 120 mph as our value for average speed and 0.5 hours as our value for time, we'll solve this problem in the next step.

• Note, however, that if the units of time used in your average speed value are different than those used in your time value, you'll need to convert one or the other so that they are compatible. For instance, if we have an average speed value that's measured in km per hour and a time value that's measured in minutes, you would need to divide the time value by 60 to convert it to hours.
• Let's solve our example problem. 120 miles/hour × 0.5 hours = 60 miles . Note that the units in the time value (hours) cancel with the units in the denominator of the average speed (hours) to leave only distance units (miles).

• For instance, let's say that we know that a car has driven 60 miles in 50 minutes, but we don't have a value for the average speed while traveling. In this case, we might isolate the s avg variable in the basic distance equation to get s avg = d/t, then simply divide 60 miles / 50 minutes to get an answer of 1.2 miles/minute.
• Note that in our example, our answer for speed has an uncommon units (miles/minute). To get your answer in the more common form of miles/hour, multiply it by 60 minutes/hour to get 72 miles/hour .

Joseph Meyer

To solve an equation for a variable like "x," you need to manipulate the equation to isolate x. Use techniques like the distributive property, combining like terms, factoring, adding or subtracting the same number, and multiplying or dividing by the same non-zero number to isolate "x" and find the answer.

• For instance, in the example problem above, we concluded that to travel 60 miles in 50 minutes, we'd need to travel at 72 miles/hour. However, this is only true if travel at one speed for the entire trip. For instance, by traveling at 80 miles/hr for half of the trip and 64 miles/hour for the other half, we will still travel 60 miles in 50 minutes — 72 miles/hour = 60 miles/50 min = ?????
• Calculus-based solutions using derivatives are often a better choice than the distance formula for defining an object's speed in real-world situations because changes in speed are likely.

Finding the Distance between Two Points

• Note that this formula uses absolute values (the " | | " symbols). Absolute values simply mean that the terms contained within the symbols become positive if they are negative.
• d = |x 2 - x 1 |
• = |-6| = 6 miles .

• The 2-D distance formula takes advantage of the Pythagorean theorem , which dictates that the hypotenuse of a right triangle is equal to the square root of the squares of the other two sides.
• For example, let's say that we have two points in the x-y plane: (3, -10) and (11, 7) that represent the center of a circle and a point on the circle, respectively. To find the straight-line distance between these two points, we can solve as follows:
• d = √((x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 )
• d = √((11 - 3) 2 + (7 - -10) 2 )
• d = √(64 + 289)
• d = √(353) = 18.79

• For example, let's say that we're an astronaut floating in space near two asteroids. One is about 8 kilometers in front of us, 2 km to the right of us, and 5 miles below us, while the other is 3 km behind us, 3 km to the left of us, and 4 km above us. If we represent the positions of these asteroids with the coordinates (8,2,-5) and (-3,-3,4), we can find the distance between the two as follows:
• d = √((-3 - 8) 2 + (-3 - 2) 2 + (4 - -5) 2 )
• d = √((-11) 2 + (-5) 2 + (9) 2 )
• d = √(121 + 25 + 81)
• d = √(227) = 15.07 km

Calculator, Practice Problems, and Answers

Community Q&A

You Might Also Like

• ↑ https://www.khanacademy.org/math/basic-geo/basic-geometry-pythagorean-theorem/pythagorean-theorem-distance/v/distance-formula
• ↑ https://www.geeksforgeeks.org/time-speed-distance
• ↑ https://www.purplemath.com/modules/distform.htm
• ↑ https://www.mathsisfun.com/algebra/distance-2-points.html
• ↑ https://www.khanacademy.org/math/basic-geo/basic-geometry-pythagorean-theorem/pythagorean-theorem-distance/v/example-finding-distance-with-pythagorean-theorem
• ↑ https://www.math.usm.edu/lambers/mat169/fall09/lecture17.pdf
• ↑ https://www.calculatorsoup.com/calculators/geometry-solids/distance-two-points.php

About This Article

To calculate distance, start by finding the average speed the object traveled and the amount of time it was traveling for. Make sure you're using the same units for the average speed and time or else your calculation won't be accurate. For example, if you're using miles per hour for the speed, you would need to use hours, not minutes or seconds, for the time. Once you have your 2 values, just multiply them together to get the distance the object traveled. To learn how to calculate the distance between 2 points, scroll down! Did this summary help you? Yes No

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• Formula of Speed Time and Travelled Distance

Introduction of Speed, Distance and Time

‘Speed, distance, time’ is one of the famous and important topics within the maths or quantitative field of any competitive exam. The concept of velocity, time, and distance is used drastically for questions referring to specific topics inclusive of motion in a straight line, circular motion, boats, races, clocks, and many others. 

Distance, Speed, Time Formula

Students are commonly asked to determine the distance, speed, or travel time of something given any two variables. These types of problems are quite interesting to solve as it describes real-life situations for many people. For example, a question might say: 

Find the distance a car has traveled in twenty minutes at a constant speed of 50 km /hr. Generally in these problems, we use the distance speed time formula to calculate the desired quantity.

Speed 

Speed is defined as the rate at which an object moves from one place to another in a given interval of time. It is a scalar quantity as it defines only the magnitude not the directions of an object moving. The S.I. unit of speed is m/s.

The speed of a moving object can be calculated as: 

\[ Speed = \frac{Distance}{Time}\]

Speed can either be uniform or variable.

Average Speed: The average speed is the total distance covered by an object in a particular interval of time. For example,

If a moving object covers d₁, d₂, d₃...dₙ with different speeds V₁, V₂, V₃,...V n m/s in time t₁, t₂, t₃,...t n respectively, the average speed is calculated as:

\[ \frac{Total \, Distance \, Traveled}{Total \, Time \, Taken} = \frac{d_{1},d_{2},d_{3},..d_{n}}{t_{1},t_{2},t_{3},..t_{n}}\]

What is Relative Speed?

Relative speed is the speed of a moving object in terms of another. When two objects are moving in the same direction, then the difference in their speed is termed relative speed.

Similarly, when two objects are moving in different directions, then the sum of their speed is termed relative speed.

Relative Speed Formula in Time and Distance

Let us understand the relative speed formula in time and distance with an example.

If two objects are moving in the same direction at x₁ m/s and x₂ m/s, respectively, where x₁ > x₂, then their relative speed is (x₁ - x₂) m/s.

Example 1: Consider two objects X and Y separated by a distance of d meters. Suppose, If both X and Y are moving in the same direction at the same time at a speed of x meter per second and y meter per second respectively, then

Relative speed = (X - Y) metre per second

If two objects are moving in different directions at x₁ m/s and x₂ m/s, respectively, where x₁ < x₂, then their relative speed is (x₁ + x₂) m/s.

Example 2: Consider two objects X and Y separated by a distance of d meters. Suppose, If both X and Y are moving in different directions at the same time such X moves towards Y at speed of x m/s, and Y moves away from X at a speed of y m/s, where X > Y, then, 

Relative Speed = (X + Y) metre per second

Distance refers to the length of the path covered by an object or person. You can calculate the distance traveled by an object if you know how long and how fast it moved. The distance traveled by an object or person in terms of speed and time can be calculated as: 

Time refers to the duration in hours, minutes, or seconds spent to cover a particular distance. Time taken by a moving object to cover a certain distance at a given speed is calculated as :

\[ Time = \frac{Distance}{Speed}\]

Relationship between Speed, Time and Distance

\[ Speed = \frac{Distance}{Time}\] This tells us how slow or fast an item actions. It describes the distance traveled divided by the point taken to cover the distance. 

Distance is directly proportional to speed, but time is inversely proportionate. Thus, \[ Distance = Speed * Time \]

\[ Time = \frac{Distance}{Speed}\], as the rate increases the time taken will decrease and vice versa. 

Using the precise units is critical to not forget while the usage of the formulation. 

Units for Speed, Time, and Distance

Speed, distance, and time may be expressed in one of a kind:

Time - second (sec), minute (min), hour (hr)

Distance - meter (m), kilometer (km), mile, feet

Speed - m/s, km/hr

So, if distance = kilometre and time = hour, then velocity = distance/ time; the units of speed would be km/ hr.

Units of speed, time, and distance are obvious, let us apprehend the conversions related to these.

Speed, Time and Distance Conversions

In order to convert from km/hour to m/sec, we multiply by 5/18. So, 1 km/hour = 5/18 m/sec

In order to convert from m/sec to km/hour, we multiply with the aid of 18/five. So, 1 m/sec = 18/5 km/hour = 3.6 km/hour

1 yard = 3 ft

1 kilometer= 1000 meters

1 mile= 1.6 km

1 hr = 60 minute = 3600 seconds

If the ratio of speeds is a: b for a certain distance, the ratio of time taken to close the gap may be b: a, and vice versa.

Uses of Speed, Time, and Distance

Average speed  

\[common velocity = \frac{general \, distance \, traveled}{overall \, time \, taken}\]

When the distance is consistent: common \[ velocity = \frac{2xy}{x+y}\]; where x and y are the 2 speeds at which the identical distance has been covered.

Solved Examples

A person has covered a distance of 60 km in 2 hours. Calculate the speed of the bike.

Given: Distance Covered, distance = 60 km,

Time taken, time = 2 hours

Speed is calculated using the formula: \[ Speed = \frac{Distance}{Time}\]

= 30 Km/hr.

In a bike race, a biker is moving at a speed of 80 km/hr. He has to cover a distance of 105 km. Calculate the time will he need to reach his destiny.

Given: Speed = 80 km/hr,

Distance  to cover, d = 105 km,

Taken time, t =?

Speed is given by the formula: \[ Time = \frac{Distance}{Speed}\] 

Time is taken \[ Time = \frac{Distance}{Speed}\]

Time is taken by the biker = 1.31 hr

A car person travels a car at a speed of 50 km per hour. How far can he cover in 2.5 hours?

The equation for calculating distance traveled by car, given speed and time, is 

Distance = Speed/Time

Substituting the values, we get

Hence, a car can travel 125 km in 2.5 hours.

If a boy travels at a speed of 40 miles per hour. At the same speed, how long will he take to cover the distance of 160 miles?

The formula to calculate time, when speed and distance are given is:

Time taken by car to cover 160 miles is :

\[ Time = \frac{160}{40}\]

T = 4 hours

Hence, a boy will take 4 hours to cover a distance of 160 miles at a speed of 40 miles per hour.

Two boys are running from the same place at a speed of 7 km/ hr and 5 km/hr. Find the distances between them after 20 minutes respectively if they move in the same direction.

When boys run in the same direction, 

Their relative speed = ( 7 - 5) km/ hr = 2 km/ hr.

Time is taken by boys = 20 minutes

Distance covered = Speed × Time

\[ = 20 * \frac{20}{60}\]

Hence D = 6.6 km

From this discussion, we have concluded that,

If two moving bodies are moving at the same speed, the distance traveled by them is directly proportional to the time of travel i.e when speed is constant.

If two moving bodies move for the same time, the distance traveled by them is directly proportional to the time of travel i.e when time is constant.

If two moving bodies are moving at the same distance, their travel of time is inversely proportional to speed i.e when the distance is constant.

FAQs on Formula of Speed Time and Travelled Distance

1. Who discovered the speed formula?

Galileo Galilei (Italian Physicist) is credited with being the first to measure the speed of a moving object concerning the time taken and distance covered. He defined speed as the distance covered by an object or person per unit of time.

2. What is known as instantaneous speed?

Instantaneous speed is the speed of a moving object at a specific point in time. For example, a car is presently travelling at 60 km/hr, but it may speed up or slow down in the next couple of hours.

3. What is the difference between speed and average speed?

The average speed of something is calculated by dividing the total distance travelled by the total time it took to travel that distance. The definition of speed is the rate at which anything is moving at any given time. Average speed refers to the pace at which a vehicle travels over the course of a journey.

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4.1: Relationship Between Distance, Speed, and Time

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Learning Objectives

• You will be able to distinguish among distance, speed, and time
• You will be able to convert between various units of time
• You will be able to convert between various units of speed
• You will be able to perform calculations using the relationship between distance, speed, and time
• You will know what a light-year means and how it is related to a year
• You will be able to determine the lookback time to various astronomical events, including ones occurring at different distances and times

What Do You Think: How Long to Get There

Distance, speed, and time.

Before we can apply the concepts of distance, speed, and time to the Universe, we must understand the specific meaning of each and examine how they are related.

Distance can be defined as how far apart two objects are in space. For example, the distance between Chicago and San Francisco is about 2,100 miles (about 3,400 km). As we discussed in Chapter 1, the distances involved in astronomy are so large that special distance units are often used for convenience. For example, Earth is about 150 million km from the Sun (93 million miles). This distance is called 1 astronomical unit (AU), a unit of measure invented specifically for astronomy.

Other units used specifically by astronomers to measure distance include light-years (ly), light-hours, light-minutes, and light-seconds. The light-minute is how far light travels in 1 minute. For example, Earth is about 8 light-minutes from the Sun (it takes 8 minutes for the light to travel from the Sun to Earth), so an astronomical unit is also 8 light-minutes. We often find it convenient to measure distances in the Solar System in terms of light-minutes, or even light-hours, the distance light travels in 1 hour.

A light-year is the distance light travels in a vacuum (empty space) in 1 year. In SI units, a light year is 9.5 × 10 15 m. The light-year is used to measure large distances, those beyond our Solar System. We generally use light-years to measure distances to other stars in our Galaxy, or even to galaxies beyond our own. For example, the distance across the disk of the Milky Way Galaxy is about 100,000 light-years, and the nearest major galaxy to ours (Andromeda, or M31) is 2.5 million light-years away.

Another unit that astronomers use is the parsec (pc). A parsec is equal to 3.26 light-years, and so it is also used to describe large distances. Parsec is usually accompanied by Greek prefixes, such as kilo (10 3 ) and Mega (10 6 ), to mean a thousand parsecs or a million parsecs. When abbreviated, these units are written as kpc and Mpc, just as km is a thousand meters and MW is a million watts. Therefore, the distance across the disk of the Milky Way can be described as 100,000 light-years or as 30 kpc (30,000 parsecs).

Time is a measure of how long it takes for an event to occur, or its duration. It is an observed phenomenon that we use to describe past, present, and future events. Intervals of time are usually measured in units that are convenient to the events in our daily lives. These are the familiar measurements of years, months, weeks, days, hours, minutes, and seconds. For shorter times, we can again use Greek prefixes, so that a millisecond (ms) is one thousandth of a second. For longer times, we use the year: it takes 1 year—about 365 days—for Earth to travel around the Sun one time. Humans use the year to measure the age of people and things—including the Universe itself. We can also add the Greek prefixes to the year; for example, a Gyr (Gigayear) is 1 billion years.

Speed is defined as the rate that an object travels through space; it is the distance traveled in a certain amount of time. A familiar example from our daily lives can be seen when we drive to work or school. Our speed is measured by how fast or slowly we drive. Our car is said to have a speed of 60 miles per hour (mph) if it will travel a distance of 60 miles in exactly 1 hour.

Velocity is another term that you will see in the activities below. Velocity can be simply defined as speed in a particular direction. In the above example for speed, we said that a car travels at a speed of 60 mph. If we add a direction, say the car is traveling north at 60 mph, we then have the car’s velocity: A car traveling 60 mph north is different from a car traveling 60 mph west. Both travel the same distance, 60 miles, in 1 hour, but if they start at the same spot, they will certainly arrive at different destinations! It is this difference that velocity takes into account.

Mathematically, velocity is often represented by the letter \(v\) as seen in the equation:

\[v⃗ =\dfrac{d⃗}{ t}\nonumber \]

which means that velocity equals displacement (change of position) divided by time. Here, the v and d have arrows above them to remind us that they include the direction traveled.

Having made the distinction between speed and velocity, we must warn you that people often say velocity when they really mean speed. For instance, when discussing planets orbiting the Sun, or the flight path of rockets and other spacecraft, we might refer to their velocity when we really have no interest in the direction of travel. Fortunately, it is generally easy to tell from the context if the direction as well as speed is important.

In physics and astronomy, the speed of light plays an important role in understanding how our Universe works. Light-speed is the rate that light travels through empty space (a vacuum), which is about 3.0 × 10 8 m/s or 3.0 × 10 5 km/s. It is represented by the symbol c , and measurements show it to be constant—it does not change, regardless of the state of motion of either its source or the one measuring it.

Using the mathematical relationship between velocity, distance, and time is how we find the equivalent distances of light-minutes and light-years in SI units. Using the previous equation, and ignoring the arrows in this example because we are not concerned about direction, we can determine how far the light year and light minute are in meters:

\[v = \dfrac{d}{t}\nonumber \]

Rearranging,

\[d = v × t\nonumber \]

Plugging in values,

\[\begin{align*} 1\, \text{light-minute} &= (3 × 10^8 meters/\cancel{second}) × (60\, \cancel{seconds}) \\[4pt] &= 1.8 × 10^{10}\, meters. \end{align*} \]

\[\begin{align*} 1\, \text{light-year} &= (3 × 10^8 meters/\cancel{second}) × (1 \cancel{year} × 3.15 × 10^7 \cancel{second}/\cancel{year}) \\[4pt] &= 9.5 × 10^{15}\, meters \end{align*} \]

Play Animation        Play Animation

Keep the definitions of time, distance, and speed, and of the relationships between them, in mind as you work through the activities that are presented in the following sections.

Powers of Ten: Timescales

In this activity, you must drag and drop the tiles from the right-hand side of the screen into the correct open space in the table.

The first column gives a physical description of a time span, the second is the measurement of that time span in convenient units, and the third represents the time span expressed in seconds using scientific notation.

You will know you have dragged the tiles into the correct space when you see a green check mark.

Play Activity

The previous activity gave you a chance to think about some different timescales you might encounter in your daily life or as part of this class. It asked you to compare them and rank them. This is a useful skill to have when you are trying to understand how one process or event might relate to another. However, in the previous activity, you were given all of the times in a common unit, seconds. Normally, things are not so convenient. You will generally have to convert to a common unit before you can make a comparison. The next set of activities gives you additional practice with this useful skill 

Unit Conversions: Time

In the next set of activities, you will work with the relationship between distance, speed, and time. These quantities can be described in various ways. For instance, speed can be miles per hour (mi/hr or mph) or kilometers per second (km/s), or even furlongs per fortnight! The important thing is that speed is always the ratio of a distance traveled to the time needed to travel that distance: distance/time. While the units we use to describe a speed are arbitrary, we generally use whatever is most convenient. The next several activities are intended to give you a better understanding of speed and its relation to distance and time.

DISTANCE, TIME, AND SPEED IN EVERYDAY LIFE

Worked Example:

1. If you have been driving on the highway for 1 hour and have traveled 30 miles, what is your average speed?

• Find: \(v\)
• Given: t = 1 hour, d = 30 miles
• Concept(s): \(v = d/t\)
• Solution: \(v\) = 30 miles/1 hour = 30 miles/hour

B. Distance

1. If you have been driving on the highway at 60 miles/hour for 2 hours, how far have you traveled?

• Find: \(d\)
• Given: t = 2 hours, v = 60 miles/hour
• Concept(s): \(v = d/t → d = vt\)
• Solution: \(d\) = (60 miles/ hour )(2 hours ) = 120 miles

C. Travel Time

1. If you have been driving on the highway at 20 miles/hour and have traveled a total of 80 miles, how much time have you been traveling?

• Given: d = 80 miles, v = 20 miles/hour
• Concept(s): v = d/t → t = d/v
• Solution: d = (80 miles )/(20 miles /hour) = 4 hours

HOW MUCH TIME TO GET THERE

Now the goal is to determine how much time it would take you to get to various places in the Universe, if you were traveling on foot (if it were possible!), in our current fastest spaceship, at the speed of light, or at half of the speed of light.

Assume the following speeds:

• Speed of a person walking: about 3 miles/hour = 5 km/hour
• Speed of our fastest spaceship: 10 miles/second = 16 km/second = 57,600 km/hour
• Speed of light: 186,000 miles/second = 300,000 km/second
• Half of the speed of light: 93,000 miles/second = 150,000 km/second

Drag and drop the travel time tiles for the following places you might like to visit. Their distances are:

• Moon : 240,000 miles
• Nearest star (Proxima Centauri): 4 light-years
• Across the Galactic Disk : 100,000 light-years across
• Nearest galaxy : 2.5 million light-years

There are several worked examples below to get you started. All of the times can be calculated based on the concept that speed = distance

time ( v = d/t ), or equivalently, that time = distance/speed ( t = d/v ).

Worked Examples:

1. How much time would it take to walk to the Moon, if you could?

• Given: Use the facts that the distance d to the Moon is about 240,000 miles, and the typical person can walk at a speed, v, of about 3 miles/hour (without breaks).
• Concept(s): Use the concept that v = d/t → t = d/v.
• Solution: Put in the known numbers: t = d/v = (240,000 miles ) / (3 miles /hour).
• Cancel miles, and use calculator: t = 80,000 hours.
• Convert hours to years: t = 80,000 hours × (1 day /24 hours ) × (1 year/365 days) = 9 years.

2. How much time would it take to get to the nearest star (4 light-years away) traveling at light-speed?

• Given: d = 4 light-years, v = speed of light
• Concept(s): t = d/v

Solution: (4 light-years) / (1 light-year/year) = 4 years.

3. How much time would it take to get to the nearest star (4 light-years away) traveling at half light-speed?

• If you are going at half of the speed of light, that means you are going slower by a factor of 2. That means it will take you 2 times longer than if you were traveling at light-speed.
• 4 years × 2 = 8 years.

Now you are ready to fill in the chart.

Lookback Time - Looking Far Away is Looking Back in Time

What do you think: light-years.

The Stargazers Club is discussing a galaxy that is far, far away. Keisha has pulled up an image of it on her phone and tells the group that it is 10 billion light-years away.

• Indira: “That means we’re seeing the galaxy as it looked 10 billion years ago, when it was very young. It probably looks a lot different now.”
• Jason: “Light-years is the amount of time it takes the light to get to us, right?”
• Keisha: “If the galaxy is 10 billion light-years away, then it must be 10 billion years old.”

The distances to stars and galaxies are so large that even light, traveling almost 300,000 km every second, still requires years to travel to them. That means when we look at a star, Alpha Centauri for example, we are not seeing it as it is. We are seeing it as it was 4 years ago . The same is true for the Sun, of course. We do not see it as it is, we see it as it was 8 minutes ago. That has certain implications for our observations of the Universe; if the Sun were to shut off at this moment, we would not know it for 8 minutes. That is because any photons that just left the Sun would not arrive for 8 minutes, and until they got here we would have no way to know that the Sun had gone out.

This concept is so important in astronomy that it is given a special name: lookback time. We would say that the lookback time to the Sun is 8 minutes. To Alpha Centauri, the lookback time is about 4 years. But what about other parts of the Milky Way Galaxy, or other galaxies? Well, the typical lookback time to objects inside our Galaxy is several tens of thousands of years. That is because our Galaxy is about 100,000 light-years across. As a result, light requires up to about 100,000 years to reach one part of the Galaxy from another part. For external galaxies, the lookback times are even bigger.

The nearest large galaxy to the Milky Way is M31, the Andromeda Galaxy. This galaxy is about the same size as ours, but it lies about 2.5 million light-years away. So, if you go out tonight and find M31 (it can be seen from the northern hemisphere in the late summer or fall if you know where to look), the glow you see will have begun its journey 2.5 million years ago. Think about that for a moment. When that light started out, human beings ( Homo sapiens ) did not yet exist as a species. Parts of the Coast Range of California were still pushing upward from the sea, the current volcanoes of the Andes mountains and the Cascades had not yet grown, and the island of Hawaii was still hidden below the Pacific waves.

Still, if we could somehow violate the laws of physics and see M31 as it is right now, we would see very few differences between now and 2.5 million years ago. Galaxies do not change very much over such a time period, unlike Earth and its living creatures. However, if we look at even more distant objects, and that includes all galaxies, then the lookback time is greater. Nearby galaxies are tens of millions of light-years away, and the most distant galaxies are billions of light-years distant. We are seeing those galaxies, the nearest of them, as they were tens of millions of years ago. For the most distant galaxies, we see them as they were billions of years ago. Even for a galaxy, a billion years is a long time. In fact, the lookback time for the most distant galaxies goes back to nearly the beginning of the Universe. (Did you know that the Universe had a beginning?) In a sense, the finite speed of light turns the entire Universe into a time machine, allowing us to see its history.

Lookback Time and Units

In this activity, we will review measures of distance and time that are typically used by astronomers.

A. Basic definitions

B. observing an astronomical event.

In 1994, scientists were amazed and thrilled to watch pieces of Comet Shoemaker-Levy 9 hit the planet Jupiter. Tremendous explosions resulted, creating plumes many thousands of kilometers high, hot “bubbles” of gas in the atmosphere, and large dark “scars” on the atmosphere that lasted for weeks. At the time, NASA’s Galileo satellite was about 1.6 AU from Jupiter, and the Voyager 2 satellite was at a distance of 42 AU from Jupiter (on its way out of the Solar System).

Hints: Recall that 1 AU = 8.3 light-minutes. Also, when speed is the speed of light, if the distance is in light-minutes, the time is in minutes. (The same is true for light-years and years.)

C. Communicating with satellites

In 2003, NASA sent missions to Mars that placed the rovers Spirit and Opportunity on the surface of the planet.

Hints: Recall that 1 AU = 8.3 light-minutes = 150 million km.

1. The closest distance from Earth to Mars is about 55 million km. At this distance, how much time does it take for radio control signals from Earth to reach Spirit? Round to the nearest minute.

LOOKBACK TIME

In this activity, you should see a star field. In the center is the Observer star. Around the Observer star are various other stars that may go supernova (explode). In fact, three of them are going to go supernova, and you need to figure out the order that the Observer star will see them.

When you select the “next” button in the bottom right, the “event order” field at the top will be filled out. The “event order” displays the three stars in the star field that will go supernova. Also displayed is the timeline for when the stars explode. The first star explodes at time zero and starts the clock running.

Find the stars that will go supernova in the star field and hover your cursor over them. This displays the distance to the star from the Observer star in light-years. This distance corresponds to its lookback time in years. For example, Star D is 1.75 light-years from the Observer star, which means that if it were to go supernova, 1.75 years would pass before the Observer would see it. The lookback time is 1.75 years for that star.

Determine the order in which the Observer will see the three supernovae based on the time between each supernova and the distance from the Observer star.

Once you have made your selections in the “observation order” drop-down boxes, click the “next” button again and watch the supernovae.

As each supernova is seen by the Observer star, their order will be indicated at the bottom, over your selections. Once all three supernovae have been observed by the Observer star, the application will let you know if you were correct or not.

Click the “next” button to start another round.

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Speed, Distance, and Time are the three most important physical quantities which are of utmost importance in Kinematics. The three quantities Speed, Distance, and Time are related to each other through a unique relation called as Time Speed Distance Formula abbreviated as TSD Formula. The Speed Distance Time formula will help us to calculate the speed, time taken, and distance travelled by a body under different conditions when any one of them is missing.

The Time Speed Distance formula will also help us to calculate the average speed for the journey and many more parameters. In this article, we will about what is speed, what is distance, and what is time, and also learn Speed Distance Time Formula to calculate the values of these three parameters under different conditions.

What is Distance?

Distance is basically the length of the path between two points on a plane. It is dimensionally equal to length which is one of the seven fundamental quantities. Hence the SI unit of distance is a meter ‘m’ but smaller units are centimetres (cm) and larger units are kilometres (km), Miles, etc. The other units of distance are light years which is used to measure the distance between two astronomical bodies. 1 light year is equal to 9.461 ⨯ 10 12 km. Nautical Mile is also a unit of distance that is used to measure distance in marine and air navigation based on Earth’s latitude and longitude. 1 Nautical Mile is equal to 1.852 km.

The distance may not be given in the desired unit, hence one needs to learn the conversion of distance from one unit to other units. For Example, if you need to convert Km to m, multiply km by 1000, and if want to convert m to km, divide by 1000.

Distance vs Displacement

Distance and Displacement are dimensionally the same quantity with some basic differences. They have the same unit i.e. m or km. The difference between Distance and Displacement is tabulated below:

Read more about Distance and Displacement .

What is Time?

Time is basically the advancement of incidents. Time is one of the most fundamental quantities out of the seven fundamental quantities defined by science. Time is recorded on Earth with respect to the rotation and revolution of Earth. Early man used to observe the time with the position of the sun in the sky. Later on, sand clocks developed which were followed by mechanical clocks and so on. Time is dimensionally represented as [T]. The SI unit of Time is Second(s). The larger units of Time are minutes and hours. In an hour there are 60 minutes and there are 60 seconds in a minute. A day consists of 24 hours.

What is Speed?

Speed is the rate of covering distance per unit of time. Speed basically tells how fast or slow a body is travelling. Mathematically, Speed is given as the ratio of Distance and Time. Speed is not a fundamental quantity instead it is a derived quantity. Since speed is the ratio of distance and time, the unit of speed is m/s which is the ratio of the SI unit of Distance and Time. The larger units of speed are Km/h and m/min. The dimensional formula of speed is [LT -1 ]

Speed vs Velocity

Speed is the rate of covering distance irrespective of direction while velocity is the rate of covering distance in a particular direction. Speed and Velocity are the same quantities in terms of physical dimension but they are different in their nature. The unit of both Speed and Velocity is m/s. The difference between speed and velocity is tabulated below:

Read more about Speed and Velocity .

Time Speed and Distance Formula

The three physical quantities time, speed, and distance are related to each other through a formula called Time Speed Distance Formula. The Speed Distance Time Formula is given as:

Speed = Distance/Time OR s = d/t Where, s is speed or velocity, d is Distance, and t is Time.

Relationship between Speed, Distance and Time

Based on the above formula, the relationship between Speed, Distance, and Time is discussed below:

• Speed is the rate of covering distance per unit of time, hence Speed = Distance/Time. The SI unit of speed is m/s.
• Time is the duration in which a particular distance is covered travelling at a given speed, thus Time = Distance/Speed. The SI unit of Time is second(s).
• Distance is the path covered by a body moving at a given speed for a given period of time. Hence, the formula for distance is given as Distance = Speed ⨯ Time. The unit of distance is m or km.
• Distance and Time are directly proportional to each other. It means if a body is travelling at a given speed then as the time increases, distance cover will also increase.
• Distance and Speed are directly proportional to each other. It means in a certain duration of time, a body travelling at a larger speed will travel a larger distance.
• Speed and Time are inversely related to each other. It means, the larger the speed lower will be the time taken to cover a specific distance.

Average Speed

Average Speed is defined as the ratio of the total distance travelled in the total duration of time. In real life scenario, the speed doesn’t remain the same, hence we can’t tell the speed with which we completed our journey. So for this purpose, the concept of average speed was introduced. Its unit is the same as that of speed and it is also a scalar quantity.

Average Speed Formula

The average speed formula is given as

Average Speed = Total Distance Travelled/Total Time Taken OR Average Speed = d 1 + d 2 + d 3 + …. + d n / t 1 + t 2 + t 3 + … + t n Where, d 1 , d 2 . . . d n are distances travelled, and t 1 , t 2 . . . t n is the time taken during the travelled distance.

Learn more about Average Speed Formula .

Relative Speed Formula

When two bodies are in motion then the speed of one body with respect to another body is called Relative Speed. The Relative Speed Formula for different cases is mentioned below:

Relative Speed Between Trains

In this heading, we will learn Relative Speed between trains travelling in the same and opposite directions. It should be noted that when two crosses each other whether in the same or opposite direction, the total distance is given by summation of the length of two trains.

Relative Speed Between Trains Travelling in the Same Direction: In this case, the relative speed between is given by the summation of speeds of individual trains. Hence, the time taken to cross two trains travelling in the same direction is given by

Time taken by two trains traveling in same direction = Sum of length of two trains/Sum of speed of two trains

Relative Speed Between Trains Travelling in Opposite Directions: In this case, the relative speed is given by the difference of speed of two trains. Hence, the time taken to cross two trains travelling in the opposite direction given by

Time taken by two trains traveling in opposite direction = Sum of length of two trains/Difference of speed of two trains

Relative Speed Between Man and Train

For a man running parallel to a moving train, the relative speed is given by the sum of the speed of man and the train if both are running in the same direction, and the relative speed is given as the difference between the speed of man and a train if they are moving opposite to each other. It should be noted that the distance to be crossed is equal to the length of the train only.

Time taken to cross each other when man is running in train’s direction = Length of train/Sum of Speed of Train and Man

T ime taken when train and man running in opposite to each other = Length of train/Difference of Speed of Train and Man

Learn more about Relative Motion .

Unit Conversion

The three quantities, Speed, Distance and Time may or may not be in standard units or you may be asked to calculate a problem in a particular unit. Hence for this purpose, we need to learn unit conversion.

Unit Conversion Length (Distance)

For this, the relation between some units should be memorized.

• 1 km = 1000m
• 1m = 1000mm
• 1mile = 1.6km
• 1nautical mile = 1.852km

The above relation must be remembered to convert the units. To convert units from larger units to smaller units we multiply and to convert from smaller units to larger units we divide. For Example, if we want to convert 2 km into m we will multiply 2 by 1000 as 1 km = 1000 m and we are converting from km to m. Hence, 2 km = 2 ⨯ 1000 m = 2000 m. If we have to convert m to km i.e. from a smaller unit to a larger unit we divide. Hence, 500 m = 500/1000 km = 0.5km

Learn more about the System of Units .

Time Unit Conversion

For time unit conversion we need to memorize the following relation between units of time

• 1 hour = 60 minutes
• 1 minute = 60 seconds
• 1 hour = 3600 seconds
• 1 day = 24 hours

Here, also we perform the multiplication for conversion from a larger unit to a unit and division from a larger unit to a smaller unit. For Example, 2 hr = 2 ⨯ 60 = 120 min and 120 min = 120/60 = 2 hours

Unit Conversion Speed

The SI unit of speed is m/s. We also use km/h as a unit of speed. If the speed is given in m/s multiply it by 18/5 to convert it into km/h and if the speed is given in km/h multiply by 5/18 to convert it into m/s.

• m/s ⨯ 18/5 = km/h
• km/h ⨯ 5/18 = m/s

Equations of Motion Acceleration Force

Sample Problems on Speed Time and Distance Formula

Problem 1: Calculate the distance travelled by truck with a speed of 6 km/hr in 1 hour.

Given: s = 6 km/hr. , t = 1 hour The distance speed time formula states that: s = d/t ⇒ d = s × t = 6 km/hr × 1 hr. = 6 km

Problem 2: A car has covered 90 km in 2 hours. What is its speed?

Given: d = 90 km , t = 2 hours The distance speed time formula states that: s = d/t = 90 km/ 2 hours = 45 km/hr

Problem 3: Find the time taken by a cyclist to cover 4 km at a speed of 10 km/hr.

Given: d = 4 km, s = 10 km/hr. The distance speed time formula states that: s = d/t ⇒ t = d/s = 4 km/ 10 km/hr = 0.4 hr = 24 minutes

Problem 4: Calculate the distance travelled by truck with a speed of 3 km/hr in 8 hours.

Given: s = 3 km/hr. , t = 8 hour The distance speed time formula states that: s = d/t ⇒ d = s × t = 3 km/hr × 8 hr. = 24 km

Problem 5: Calculate the distance travelled by truck with a speed of 18 km/hr in 8 hours.

Given: s = 18 km/hr, t = 8 hours The distance speed time formula states that: s = d/t ⇒ d = s × t = 18km/hr × 8 hr. = 144 km

Problem 6: Imagine the distance is doubled and the time is halved, what will be the new speed?

Suppose, the speed was “s” earlier, time was “t” earlier, distance was “d”. s = d/t ⇢ (1) New distance = 2d New time = t/2 New speed = s’ = 2d/(t/2) s’ = 4d/t s’ = 4s The new speed will be 4 times the old speed.

FAQs on Speed Time Distance Formula

Q1: how to find distance with speed and time.

Distance is given as the product of Speed and Time i.e. Distance = Speed ⨯ Time

Q2: What is Time Speed Distance Formula?

The Time Speed Distance Formula is the relation between Speed Distance and Time. The Speed Distance Time Formula is given as Speed = Distance/Time

Q3: How to get Time with Speed and Distance?

The Time can be calculated as Time = Distance/Speed

Q4: What is the Unit of Speed?

The unit of speed is m/s. Another unit of speed is km/h

Q5: What is Average Speed?

Average Speed is the total distance travelled by a body divided by the total time taken.

Q6: What is the Unit of Average Speed?

The unit of Average Speed is same as that of speed i.e. m/s.

Q7: What is the difference between Speed and Velocity?

The basic difference between speed and velocity is that speed is a scalar quantity and it is always non-negative but velocity is a vector quantity and it can be negative.

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