Read journeys, tariffs and conversions from graphs, and interpret the gradient as a rate such as speed or price per unit. It is on Foundation and Higher, aimed at grade 4. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A real-life graph is a story: distance–time, conversion, filling a tank. Gradient is a rate (speed, cost per unit, litres per second). A horizontal section is a stop or a constant value. A steeper line is a faster rate. Read scales — they rarely go up in 1s.
Distance–time: speed =timedistance on that section. A return journey goes back down towards zero distance-from-home. Conversion graphs: read from one axis to the line to the other axis, with a ruler. Always include units in the sentence you write as the answer.
Gradient is a rate: km per hour, pounds per unit, litres per minute. A horizontal section is a stop (distance not changing) or a constant cost. Convert minutes to hours before you divide into km/h.
Objectives
Distance is usually up the side. Time is along the bottom.
Speed = distance ÷ time, which is the gradient of that section.
A horizontal line has gradient 0.
Key points
Read values off a graph accurately, using the scale on both axes.
Work out speed from a distance–time graph as distance ÷ time for a straight section.
Describe what a flat (horizontal) section and a steeper section mean in context.
Find the gradient and intercept of a straight-line tariff graph and say what they mean.
Worked examples
Example 1
A straight section of a distance-time graph covers 40 metres in 5 seconds. What is the speed in metres per second?
2 marks
Speed = distance ÷ time = 40 ÷ 5.
40 ÷ 5 = 8.
The speed is 8 m/s.
Answer: 8
Common slips
Slip: Speed = distance ÷ time = 42 ÷ 5. That changes a number from the question, so it answers a different question.
Slip: 40 × 5 = 200. That uses multiplication, but this step needs division.
Slip: The speed is 12 m/s. That does not match the working above it.
Example 2
On a distance-time graph the line is horizontal from t = 3 minutes to t = 12 minutes. For how many minutes is the object stopped?
1 marks
Horizontal from 3 minutes to 12 minutes means the object is stopped.
12 − 3 = 9.
The object is stopped for 9 minutes.
Answer: 9
Common slips
Slip: Horizontal from 5 minutes to 12 minutes means the object is stopped. That changes a number from the question, so it answers a different question.
Slip: 12 + 3 = 15. That uses addition, but this step needs subtraction.
Slip: The object is stopped for 13 minutes. That does not match the working above it.
Example 3
A straight section of a distance-time graph goes from (2, 10) to (5, 25). Time is in seconds and distance is in metres. What is the speed in metres per second?
3 marks
Change in distance = 25 − 10 = 15.
Change in time = 5 − 2 = 3.
Speed = 15 ÷ 3 = 5.
Answer: 5
Common slips
Slip: Change in distance = 27 − 10 = 15. That changes a number from the question, so it answers a different question.
Slip: Change in time = 8 − 2 = 3. That changes a number in the working, so the step no longer follows from the one before.
Slip: Speed = 19 ÷ 3 = 5. That does not match the working above it.
Questions and answers
GCSE Maths real-life & distance–time graphs questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
A distance-time graph falls from 50 metres at 20 seconds to 20 metres at 25 seconds. What is the speed on the way back, in metres per second?
Show answer
Answer: 6
Distance covered = 50 − 20 = 30.
Time taken = 25 − 20 = 5.
M1 — Distance covered = 50 − 20 = 30.
A1 — Answer 6
Question 2 Easy2 marks
A section of a distance-time graph covers 4 km in 12 minutes. What is the speed in km/h?
Show answer
Answer: 20
12 minutes = 12 ÷ 60 = 0.2 hours.
Speed = 4 ÷ 0.2 = 20.
M1 — 12 minutes = 12 ÷ 60 = 0.2 hours.
A1 — Answer 20
Question 3 Medium2 marks
On a distance-time graph the line is horizontal from t = 5 minutes to t = 11 minutes. For how many minutes is the object stopped?
Show answer
Answer: 6
Horizontal from 5 minutes to 11 minutes means the object is stopped.
11 − 5 = 6.
M1 — Horizontal from 5 minutes to 11 minutes means the object is stopped.
A1 — Answer 6
Question 4 Medium2 marks
A distance-time graph falls from 120 metres at 25 seconds to 30 metres at 40 seconds. What is the speed on the way back, in metres per second?
Show answer
Answer: 6
Distance covered = 120 − 30 = 90.
Time taken = 40 − 25 = 15.
M1 — Distance covered = 120 − 30 = 90.
A1 — Answer 6
Question 5 Hard2 marks
A straight section of a distance-time graph goes from (3, 10) to (7, 30). Time is in seconds and distance is in metres. What is the speed in metres per second?
Show answer
Answer: 5
Change in distance = 30 − 10 = 20.
Change in time = 7 − 3 = 4.
M1 — Change in distance = 30 − 10 = 20.
A1 — Answer 5
Question 6 Hard2 marks
On a distance-time graph the line is horizontal from t = 6 minutes to t = 14 minutes. For how many minutes is the object stopped?
Show answer
Answer: 8
Horizontal from 6 minutes to 14 minutes means the object is stopped.
14 − 6 = 8.
M1 — Horizontal from 6 minutes to 14 minutes means the object is stopped.
A1 — Answer 8
Question 7 Exam-style3 marks
A distance-time graph falls from 120 metres at 20 seconds to 30 metres at 35 seconds. What is the speed on the way back, in metres per second?
Show answer
Answer: 6
Distance covered = 120 − 30 = 90.
Time taken = 35 − 20 = 15.
Speed = 90 ÷ 15 = 6.
M1 — Distance covered = 120 − 30 = 90.
M1 — Time taken = 35 − 20 = 15.
A1 — Answer 6
Common mistakes
Most lost marks on this topic are one slip.
Reading the height of the line as the speed.
The height is the distance. The gradient is the speed.
Saying a downward slope is a negative speed.
The speed is the size of the gradient. The slope tells you the direction.
Dividing time by distance.
Speed is distance divided by time.
Spot the slip
A horizontal section on a distance-time graph means
the object is stopped
the object is moving fastest
the distance is zero
Show the slip
the object is stopped Distance is not changing, so the speed is zero.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Draw the lines you use on the graph (a vertical line up and a horizontal line across) — examiners can give a mark for correct readings.
When comparing speeds, the steepest section is the fastest; you can often answer 'which part was fastest' without any calculation.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.