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Ultimate Guide to Travel Graphs| Cambridge IGCSE Mathematics

Kulni gamage.

• Created on July 20, 2023

[Please watch the video attached at the end of this blog for a visual explanation on the Ultimate Guide to Travel Graphs]

Travel graphs fall under the bigger topic of Algebra, but unlike the other lessons under this topic, this is really simple and easy to understand… as long as you read the question carefully and pay attention to the readings of the graphs ?!

What is a travel graph?

A travel graph is a line graph that tells us how much distance has been covered by the object in question within a particular time. We can use travel graphs to represent the motion of cars, people, trains, buses, etc. This means travel graphs can tell us whether an object is still (stationary), moving at a constant speed, accelerating, or decelerating.  The y -axis represents the distance travelled while the x -axis shows the time it takes to travel a distance such as that.

James went on a cycling ride. The travel graph shows James’s distance from home on this cycle ride. Find James’s speed for the first 60 minutes.

We are told that James is going on a cycling ride and that the distance he travelled is what is shown here. What is required of us is to find James’s speed for the first 60 minutes. This means you need to mark the point at 60 minutes on the x -axis as shown in the picture below.

We have learnt when learning about Speed, Time and Distance that speed = distance/ time.

Therefore, in a distance-time graph, the slope that we see (also called the gradient) is what will give us the speed.

We can see that this particular cycle has travelled 12 km in 60 minutes.

When we substitute these values into the formula above, it would look like this:

When this formula is solved, then we get James’s speed for the first 60 minutes , which is 0.2 km/min .

A train journey takes one hour. The diagram shows the speed-time graph for this journey. Calculate the total distance of this journey.

We need to be careful here because this time what we have in this question is a speed-time graph and not a distance-time graph.

In a speed-time graph, the gradient of a slope represents either acceleration or deceleration, which will be concepts touched upon in later lessons. The distance travelled is found by calculating the area under a speed-time graph.

In order to calculate the distance travelled by the train therefore, we need to calculate the area under the graph that is drawn. To make things easier, we can separate this graph into shapes:

2 triangles and 1 rectangle

Triangle 1: Area of a triangle = ½ × base of triangle × height of triangle Area = ½ × 4 km × 3 km/min Area = 6 km2

Rectangle: Length of the rectangle can be found by finding out the difference between 50 and 4, which equals to 46 min. The height of the rectangle is 3 km/min. Area = length × base Area = 46 min × 3 km/min Area = 138 km

Triangle 2: Area of a triangle = ½ × base of triangle × height of triangle Area = ½ × 10 km × 3 km/min Area = 15 km

Total Area under the graph = Total distance travelled by the train Therefore, Total Distance = Triangle 1 + Rectangle + Triangle 2 Total Distance = 6 km + 138 km + 15 km Total Distance =  159 km

Those are the basic tips and tricks you would need to learn in this particular chapter!

Travel Graphs at Exams

Pay attention to what sort of graph is given to you. Is it a distance-time graph? A speed-time graph? Depending on the type of graph, remember, the value represented by the gradient changes, and so does the value represented by the area under the graph.

Practice as many questions as you can on this topic. They are quite simple once you get the hang of them. You can find some questions in this quiz to check where you stand!

If you are struggling with IGCSE revision or the Mathematics subject in particular, you can reach out to us at Tutopiya to join revision sessions or find yourself the right tutor for you.

Watch the video below for a visual explanation of the lesson on the ultimate guide to travel graphs!

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Travel graphs

Part of Maths Compound measures

A travel graph is a line graph which describes a journey – it shows how distance changes with time.

Time is always represented on the x-axis and distance on the y-axis .

The distance is always distance from a particular place and the time is the time from the start of the journey.

Emily cycles from her house to her Nanny’s.

The graph below shows her journey.

The journey is in three parts.

Blue line – this represents the first 30 minutes of the journey. Emily is 5 km from home after 30 minutes.

Red line – the time has increased by 5 minutes, but the distance has not increased. This means Emily stopped cycling for 5 minutes.

Green line – this represents the last 25 minutes of the journey. The whole journey has taken 60 minutes and Emily is now 12 km from home.

a) What was Emily’s speed, in kilometres per hour, over the first part of the journey?

b) Did Emily cycle faster before or after she stopped for 5 minutes?

Show answer Hide answer

a) Emily cycled 5km in 30 minutes. In 60 minutes, she would cycle 10 km so her speed over the first part of the journey is 10 km/hr.

You could work out the speed after the stop but there is no need to do that.

b) Look at the blue line.

In the first 15 minutes, Emily has cycled 2.5 km.

Look at the green line.

In the first 15 of this part of the journey, Emily has cycled just over 4 km – more distance over the same time.

Emily cycled faster after she stopped for 5 minutes.

Note that the green line is steeper than the blue one.

On a travel graph, steeper lines indicate faster speeds.

The travel graph below shows the McGrath family’s car journey from their home in Ballymena to Donegal.

a) The family stopped for a cup of coffee on the way. How long did they stop for?

b) What time did they arrive at their destination?

c) Did they travel faster before or after they stopped for coffee?

a) The straight line represents the time the family stopped.

Each square on the horizontal axis represents 10 minutes.

They stopped for 4 x 10 = 40 minutes.

b) Each square on the horizontal axis represents 10 minutes.

The family arrived 20 minutes before 1700, that is 1640.

c) They travelled faster before they stopped.

The line representing the first part of the journey is steeper than the line for the third part.

Test section

Jude sets out at 1100 to walk to his friend’s house.

They chat for a while and then he walks home.

What time does Jude arrive home?

The correct answer is c) 1220.

What was Jude’s speed on the way to his friend’s house?

The correct answer is b) 4 km/hr.

How long did Jude and his friend spend chatting?

a) 2 minutes

b) 20 minutes

c) 10 minutes

The correct answer is c) 10 minutes.

What was Jude’s speed on the way back from his friend’s house?

The correct answer is a) 3 km/hr.

Where next?

Discover more about this topic from Bitesize.

Shape, space and measures

More on Compound measures

Find out more by working through a topic

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Speed, distance and time

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Distance Time

Distance Time Graph

Here we will learn about distance-time graphs, including how to interpret and construct them.

There are also distance-time graph worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What are distance time graphs?

Distance-time graphs are graphs that show the distance an object or person has travelled against time. They can also be referred to as travel graphs.

A distance-time graph will show the distance (in metres, kilometres, miles etc.) on the vertical axis ( y -axis) and the time (in seconds, minutes, hours etc.) on the horizontal axis ( x -axis).

The distance-time graphs we will look at on this page will all be drawn using straight lines.

Straight lines on a distance-time graph represent constant speeds. To find the speed from a distance-time graph you will need to be able to find the gradient of the straight lines.

The steeper the gradient , the faster the object is travelling .

One way of calculating the speed from a distance-time graph is to think about how far the object has travelled in one time unit.

For example, if an object has travelled 20 miles in 30 minutes, it would travel 40 miles in one hour, therefore the speed is 40 \ mph.

How to read distance time graphs

In order to read distance-time graphs:

Locate any relevant points from the distance-time graph.

Check the information required. For example, distance travelled at a selected time, period of being stationary, speed at a selected point in the journey.

• Use the appropriate process from the list.
• Distance travelled at a selected time – read from the vertical axis at the given time.
• Period of being stationary – find the time when the line is horizontal.
• Speed at a selected point in the journey – find the gradient of the line at that time or think how far has the object travelled in one time unit.
• Average speed for the whole journey – divide the total distance travelled by the total time.

Explain how to read distance time graphs

Distance time graph worksheet

Get your free distance time graph worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Related lessons on rates of change

Distance time graph is part of our series of lessons to support revision on rates of change . You may find it helpful to start with the main rate of change lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

• Rate of change
• Speed time graph

Reading distance time graphs examples

Example 1: finding the distance travelled from a distance-time graph.

The distance-time graph shows the journey of a person from their home.

How far away from their home are they after 1 hour and 30 minutes?

Locate 1 hour 30 minutes on the horizontal axis and go up to the graph line.

2 Check the information required. For example, distance travelled at a selected time, period of being stationary, speed at a selected point in the journey.

We require the distance travelled at that time.

3 Use the appropriate process from the list. Distance travelled at a selected time – read from the vertical axis at the given time.

Reading from the vertical axis gives a distance of 25 \ km.

Example 2: finding stationary periods from a distance-time graph

At what time did the person first stop and for how long?

Locate the points in the graph when the line changes.

We required the first period that the person was stationary.

Use the appropriate process from the list. Period of being stationary – find the time when the line is horizontal.

The person was first stationary after 30 minutes, and remained stationary for 30 minutes.

Example 3: finding the speed from a distance-time graph  

The graph shows the person taking a bus to a cafe. They then stopped at the cafe for a drink and snack. They then ran for an hour, before taking a taxi home. 

What speed was the person travelling during the taxi journey home?

The journey home began after 2 hours 30 minutes and finished at 3 hours.

We require the speed between 2.5 hours and 3 hours.

Use the appropriate process from the list. Speed at a selected point in the journey – find the gradient of the line at that time or think how far has the object travelled in one time unit.

The person travelled 30 \ km in 30 minutes, this would mean they would travel 60 \ km in 1 hour, therefore, their speed was 60 \ km/h.

We could also find this using the speed, distance, time formula,

\text{Speed}=\frac{\text{distance}}{\text{time}}=\frac{30}{0.5}=60\,\text{km/h}

(it is important to use 0.5 hours and not 30 minutes for the time).

Or we could have found the gradient of the line,

\frac{\text{Change in }y}{\text{Change in }x}=\frac{30}{0.5}=60.

Example 4: finding the average speed of the whole journey from a distance-time graph

The graph shows the person taking a bus to a cafe. They then stopped at the cafe for a drink and snack. They then ran for an hour, before taking a taxi home.

What was the person’s average speed for their whole journey?

We need to find the total distances travelled.

We required the average speed for the whole journey.

Use the appropriate process from the list. Average speed for the whole journey – divide the total distance travelled by the total time.

It is important to add all the distances travelled and find the time for the whole journey including any periods when the person was stationary.

\text{Average speed =}\frac{\text{total distance}}{\text{total time}}=\frac{60}{3}=20 \ \text{km/h.}

How to draw distance time graphs

In order to draw distance-time graphs:

Draw/label the horizontal axis for the time and a vertical axis for the distance.

Use the information about the distance or speed of the object to plot points on the graph.

Join the points with straight line segments.

Explain how to draw distance time graphs

Drawing distance time graph examples

Example 5: drawing a distance-time graph from information about distance at given times.

A car starts from home and travels at a constant speed for 30 minutes until it is 20 miles from home. It then stops for 1 hour before returning home, travelling at a constant speed for 45 minutes.

Draw a distance-time graph to represent the journey.

The car gets no further than 20 miles from home and the journey takes a total of 2 hours 15 minutes. Draw and label the vertical axis from 0 to 20 miles and the horizontal axis from 0 to 3 hours.

The car starts at home, so plot the point (0, 0).

After 30 minutes the car has travelled 20 miles, so plot the point (0.5,20).

It remains stationary for 1 hour, so plot the point (1.5,20).

It then returns home after 45 minutes, so plot the point (2.25,0).

Example 6: drawing a distance-time graph from information about speed at given times

A car leaves home at 12 : 00 and sets off at a constant speed of 30 \ mph.

At 12 : 30 the car stops for 10 minutes. It then returns home at a speed of 45 \ mph.

Draw the horizontal and vertical axes, but we will finish labelling them once we know more information about the maximum distance and times taken based on the information provided about the speed.

Plot (12 : 00,0).

The car travels at a speed of 30 \ mph between 12 : 00 and 12 : 30. \ 30 \ mph means it would travel 15 miles in 30 minutes, so we will need to plot (12 : 30,15).

The car stops for 10 minutes, so we will need to plot (12 : 40,15).

The car returns home at a speed of 45 \ mph.

You can use \text{time =}\frac{\text{distance}}{\text{speed}}=\frac{15}{45}=\frac{1}{3} \ hour, so it will take 20 mins to travel 15 miles.

We will need to plot (13 : 00,0).

Choose appropriate scales for the axes and plot the points.

Example 7: drawing a distance-time graph from information about distance and speed at given times

A person walks from home for 10 minutes to a distance of 1 \ km. They stop for 5 minutes, and then run at a speed of 8 \ km/h away from home. After 45 minutes they immediately change direction and run towards home at a speed of 7 \ km/h.

Draw a distance-time graph to represent their journey.

The person starts from home, so we will need to plot (0, 0).

The person walks from home for 10 minutes to a distance of 1 \ km, so we will need to plot (10,1).

They stop for 5 minutes, so we will need to plot (15,1).

Then run at a speed of 8 \ km/h away from home for 45 minutes. 45 minutes = 0.75 hours. Using \text{distance = speed}\times \text{time = }8\times 0.75=6 \ km.

We will need to plot (60,7).

They immediately change direction and run towards home at a speed of 7 \ km/h, they have 7 \ km to run which will take 60 minutes, so we will need to plot (120,0)

Common misconceptions

• Confusing distance-time graphs with speed-time graphs

It is common for students to confuse distance-time graphs with speed-time graphs. This may result in students just reading a value from the vertical axis instead of calculating the gradient of a distance-time graph to find a speed.

• Calculating average speed incorrectly

The average speed could be incorrectly calculated by finding the mean of the different speeds during a journey. Another incorrect method is to only use the periods when the object is moving and to forget to include the periods when it is stationary.

• Drawing impossible distance-time graphs

There are some graphs that would be impossible for a distance-time graph. For example, vertical lines would represent an infinite speed.

Objects travelling back in time.

Practice distance time graph questions

1. A horizontal line on a distance-time graph shows that …

The object is accelerating.

The object is stationary.

The object is moving at a constant speed.

The object is decelerating.

A horizontal line shows the object is covering zero distance for a period of time.

2. Which of the distance-time graphs shows an object moving at the greatest speed?

Greater speeds have a steeper gradient.

3. What is the speed of the object shown in this distance-time graph?

The object travels 40 \ km in 2 hours.

4. What is the speed of the object shown in this distance-time graph?

The object travels 120 miles in 1.5 hours, so it must travel 80 miles in 1 hour.

5. An object travels away from home at a speed of 60 \ km/h for half an hour. It then stops and remains stationary for a quarter of an hour before returning home at a speed of 40 \ km/h. Select the correct distance-time graph for the journey.

60 \ km/h for 30 minutes gives a distance of 30 \ km. \ 0 \ km at 40 \ km/h will take 45 minutes.

6. The image shows part of a distance-time graph.

The last part of the journey is for the object to return home at a speed of 80 \ km/h. Which is the correct completed distance-time graph?

40 \ km at 80 \ km/h will take 30 minutes. The journey ends after 90 minutes.

Distance time graph GCSE questions

1. A salesperson was driving on a motorway from London to York. He stopped at a motorway service station halfway into his journey.

Which of the distance-time graphs could represent his journey?

• 2. The distance-time graph shows part of a journey Sarah took on a bike ride.

(a) What did Sarah do between 09 : 45 and 10 : 00?

(b) What was Sarah’s speed between 10 : 00 and 10 : 30, in km/h?

She stopped moving/was stationary.

Process of dividing 6 \ km by 0.5 hours or equivalent method.

3. The distance-time graph shows the first part of a journey of a person on a shopping trip.

The person walked from their home to the shop and arrived at 12 : 00.

The person stays in the shop for 15 minutes and then catches a bus home.

The bus stopped outside their door and travelled at an average speed of 20 miles per hour.

(a) At what speed did they walk to the shops? Give your answer in miles per hour.

(b) Complete the distance-time graph showing the remaining parts of their journey.

Horizontal line to (12 : 15, 5).

Process to find the time for the bus ride ( 15 minutes).

Line from (12 : 15, 5) to (12 : 30,0).

Learning checklist

You have now learned how to:

• Read and interpret distance-time graphs
• Draw distance-time graphs
• Calculate speed from distance-time graphs

The next lessons are

• Conversion graphs
• Units of measurement
• Scale maths

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  Menu   Level 1 Level 2 Level 3 Level 4 Exam Help More Graphs

This is level 4; Draw a travel graph from the given description. Click on the points at the ends of where the straight line segments of the graphs should be.

This is Travel Graphs level 4. You can also try: Level 1 Level 2 Level 3

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Description of Levels

Level 1 - Reading information from distance-time graphs

Level 2 - Matching distance-time graphs with their descriptions

Level 3 - Reading information from speed-time graphs

Level 4 - Draw a travel graph from the given description

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Graphs including lesson Starters, visual aids, investigations and self-marking exercises.

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Distance-Time Graphs

For a basic introduction to distance-time graphs see Hurdles Race . For more details play the video below.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

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Notes - Graphs - 4. Travel Graphs. Powerpoint

Subject: Mathematics

Age range: 14-16

Resource type: Assessment and revision

Last updated

14 March 2013

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Maryam-Khan

Empty reply does not make any sense for the end user

phill_g_tucker

Handoutfinder.

Excellent. Although there is one mistake: says 30 minutes is a quarter of an hour when it's really half. But that's easily fixed! Keep up the good work

A comprehensive revision aid on travel graphs. It is very useful in that it drums into pupils the importance of taking time to interpret the graphs before attempting to answer questions. Provides an interesting extension which encourages pupils to think about the rate at whick different shaped glasses would fill with water.

Really useful powerpoint, mistake on slide 4 point 2 it says quarter of an hour but should say half. Very good though

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TOM ROCKS MATHS

Maths, but not as you know it…, gcse maths: travel graphs (speed-distance-time).

Learn how to use travel graphs relating speed, distance and time to solve problems. Tom introduces the topic, Bobby applies it to Usain Bolt’s 100-metre world record, and Susan uses an interactive tool on GeoGebra – go to www.geogebra.org/m/ABuBYdX7 to join in at home. 

This is the second lesson in a new series with the Maths Appeal duo – Bobby Seagull and Susan Okereke – and Tom Rocks Maths where we’ll be exploring the GCSE Maths syllabus to show the world that maths is accessible to everyone!

Watch Bobby and Susan answer YOUR questions here .

Watch Tom’s livestream here .

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