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9.6 Distance-Time Graphs

GCSE Maths Foundation · Edexcel · Chapter 9: Graphs

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: reading journeys from a graph, working out speeds and average speed, and drawing a distance-time graph. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Describe a journey from a distance-time graph
  • Work out a speed from a distance-time graph
  • Work out the average speed for a whole journey
  • Draw a distance-time graph from a description

Key words

  • Distance-time graph: A graph with time across the bottom and distance from a starting point up the side.
  • Speed: How far you travel in each unit of time, e.g. km/h (kilometres per hour) or m/s (metres per second).
  • Stationary: Not moving. The distance stays the same, so the graph is horizontal.
  • Average speed: Total distance ÷ total time for the whole journey, including stops.

Reading a distance-time graph

The graph shows Leo’s bike ride. Each small square across is 10 minutes. Each square up is 1 km.

  • A; What the graph shows up from (09:00, 0) to (09:40, 12); What Leo is doing cycling 12 km away from home
  • B; What the graph shows horizontal from 09:40 to 10:00; What Leo is doing stopped for 20 minutes, 12 km from home
  • C; What the graph shows sloping down to 0 at 11:00; What Leo is doing cycling back home

Key fact: A steeper line means a faster speed. A horizontal line means stationary. A line going down means coming back towards the start.

Speed from the graph

Key fact: Speed = distance ÷ time. On a distance-time graph, the speed is the gradient of the line.

Worked example: speeds on Leo’s ride

Part A: 12 km in 40 minutes. 40 minutes = 40/60 = 2/3 hour. Speed = 12 ÷ 2/3 = 18 km/h.
Another way: 40 minutes × 1.5 = 60 minutes, so 12 km × 1.5 = 18 km in one hour.
Part C: 12 km in 60 minutes = 12 km/h. Part A is steeper, so it is faster.

Answer: A: 18 km/h, C: 12 km/h

  • Hours; 15 1/4 = 0.25; 20 1/3; 30 1/2 = 0.5; 40 2/3; 45 3/4 = 0.75; 90 1.5

Average speed

For the whole journey use the total distance and the total time, including any stops.

Worked example: Leo’s whole ride

Total distance = 12 km out + 12 km back = 24 km. Total time = 09:00 to 11:00 = 2 hours.
Average speed = 24 ÷ 2 = 12 km/h.

Answer: 12 km/h

Drawing a distance-time graph

Work out the time and distance at the end of each part, plot those points and join them with straight lines.

Worked example: a walk

Maya leaves at 14:00 and walks 3 km at 4 km/h. She rests for 15 minutes, then walks back at 4 km/h.
Walking 3 km at 4 km/h takes 3 ÷ 4 = 0.75 h = 45 minutes, so she arrives at 14:45.
She rests until 15:00, then takes another 45 minutes to walk back, arriving at 15:45.
Points: (14:00, 0), (14:45, 3), (15:00, 3), (15:45, 0).

Answer: see the graph

Key fact: When two journeys are drawn on the same axes, the point where the lines cross shows where the two people pass each other: same place, same time.

Common mistakes

  • Dividing by minutes when the answer is in km/h. Change minutes into hours first (20 minutes = 1/3 hour).
  • Reading the time scale wrongly. Check how many minutes each small square stands for.
  • Thinking a horizontal line means moving at a steady speed. It means not moving at all.
  • Thinking a line sloping down means slowing down. It means travelling back towards the start.
  • Leaving out the stop when working out average speed. Use the total time.

Revision questions

Try these, then check your answers below each one.

Question 1. What does a horizontal line on a distance-time graph show? (Choose from: The person is not moving, The person is moving at a steady speed, The person is speeding up, The person is going back to the start.)

Answer: The person is not moving

Working: The distance stays the same while time passes, so the person is stationary.

Question 2. A cyclist travels 18 km in 45 minutes. Work out her speed in km/h.

Answer: 24 km/h

Working: 18 ÷ 0.75 = 24 km/h.

Question 3. Kim’s whole journey (6 km out and 6 km back, from 08:00 to 10:00) takes 2 hours including the stop. Work out her average speed for the whole journey in km/h.

Answer: 6 km/h

Working: 12 km ÷ 2 h = 6 km/h.

Related lessons

Continue in the full course

This lesson is section 9.6 (EGCMF0906) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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