Distance–time graphs GCSE Questions and Worked Answers
A distance–time graph pairs a time with a distance reading. On a straight section, distance change divided by elapsed time gives the rate; always check whether the axis means distance from a place or total distance travelled.
Foundation & Higher6 worked examples10 original questions
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Start with the meaning
What you need to know about distance–time graphs
A walker leaves home. Two hours later they are six kilometres along a straight route. A dot at (2, 6) records those two facts: the first number is time in hours and the second is distance from home in kilometres. Recording more dots lets us see the whole journey. A joining straight line says the distance changes at a constant rate between those times.
See the idea first
Read the journey before calculating
From 0 to 2 hours the walker moves away from home. From 2 to 3 hours the distance stays at 6 km, so they rest. From 3 to 5 hours they return along the same route. The final height is zero because they reach home, not because they have walked no distance.
This axis is distance FROM HOME, not total distance travelled. The final descending segment is the return journey; the total walk is 12 km.
From problem to method
Typical problems you need to be able to solve
These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.
Calculate a section's speed
What the problem asks: The distance rises from 2 km at hour 1 to 10 km at hour 3. Find speed.
How to solve it: The walker covers 8 km in 2 hours, so speed is 4 km/h. Subtract both starting readings; do not divide the final coordinates.
Find total distance
What the problem asks: A walker goes from home to a point 6 km away and returns along the same route.
How to solve it: Add the lengths of both journeys: 6 + 6 = 12 km. The final distance from home is zero, but distance travelled is 12 km.
Draw from a description
What the problem asks: Travel 4 km in one hour, rest half an hour, then return in one hour at constant speed.
How to solve it: Plot (0,0), (1,4), (1.5,4), (2.5,0) and join consecutive points with straight lines.
A reliable routine
Interpret a straight-route journey graph
Use this approach when the vertical coordinate records position along the route or distance from a fixed starting point. Differences between readings measure each section of the journey.
Read both axis labels, scales and units.
Split the graph where its slope changes.
Divide the magnitude of each distance change by the elapsed time to find speed.
Add distances for total travel; divide by total time, including rests, for overall average speed.
Check: A total-distance-travelled graph cannot decrease. A distance-from-home graph can decrease on a return journey. Away from a straight-route model, staying the same distance from home need not mean resting: travelling around a circle is a counterexample.
Fully worked
Distance–time graphs GCSE worked examples
Each solution explains the clue, why the method fits and how to check the result.
Example 1
Read a coordinate
2 marks
Question
Using the displayed journey graph, how far from home is the walker at 2 hours?
This axis is distance FROM HOME, not total distance travelled. The final descending segment is the return journey; the total walk is 12 km.
The point at time 2 has height 6. The walker is 6 km from home.
Example 2
Speed away
3 marks
Question
Using the same graph, find the speed during the first two hours.
This axis is distance FROM HOME, not total distance travelled. The final descending segment is the return journey; the total walk is 12 km.
Speed=(6−0)/(2−0)=3 km/h
The straight segment represents constant speed.
Example 3
A rest
2 marks
Question
For how long does the walker rest in the displayed graph?
This axis is distance FROM HOME, not total distance travelled. The final descending segment is the return journey; the total walk is 12 km.
The horizontal section runs from hour 2 to hour 3.
3−2=1 hour
Example 4
Return speed
3 marks
Question
Find speed on the return section of the displayed graph.
This axis is distance FROM HOME, not total distance travelled. The final descending segment is the return journey; the total walk is 12 km.
The distance falls 6 km in 2 hours.
Speed=6/(5−3)=3 km/h
The signed gradient is −3 km/h, but speed is positive.
Example 5
Average speed
4 marks
Question
Find the overall average speed for the displayed five-hour journey.
This axis is distance FROM HOME, not total distance travelled. The final descending segment is the return journey; the total walk is 12 km.
Distance travelled is 6 + 6 = 12 km. Include the rest in elapsed time.
Average speed=12/5=2.4 km/h
Example 6
Draw a journey
4 marks
Question
A cyclist travels 9 km from home in 30 minutes, rests 15 minutes, then returns in 45 minutes. State the points needed to draw the distance-from-home graph, assuming constant moving speeds.
Use time in minutes and distance in km. Plot (0,0), (30,9), (45,9), (90,0). Join in time order with straight lines. The rest is horizontal; the return falls.
10 original questions · total 23 marks
Distance–time graphs GCSE exam-style questions
Try each question before opening its fully worked answer. The difficulty rises through the set.
Before you startAllow about 28 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed
1
Read the axes
1 mark
What does (15, 2) mean when axes are time in minutes and distance from school in kilometres?
Show worked answer
At 15 minutes, the traveller is 2 km from school.
2
Constant speed
2 marks
Distance increases by 15 km in 3 hours. Find speed.
Show worked answer
v=15/3=5 km/h
3
Non-zero start
3 marks
A graph goes from (2, 5) to (5, 17), with hours and kilometres. Find the speed.
Show worked answer
Δd=17−5=12 kmΔt=5−2=3 hv=12/3=4 km/h
4
Minutes to hours
3 marks
A cyclist covers 8 km in 20 minutes. Find speed in km/h.
Show worked answer
20 min=1/3 hv=8÷(1/3)=24 km/h
5
Return distance
2 marks
A walker goes 7 km from home and then returns 3 km. Find total distance travelled and final distance from home.
Show worked answer
Total: 7 + 3 = 10 km. Final distance from home: 7 − 3 = 4 km, along the same route.
6
Include a stop
3 marks
A 12 km journey takes 2 hours moving and 1 hour resting. Find overall average speed.
Show worked answer
v=12/(2+1)=4 km/h
7
A total-distance graph
2 marks
Could a total-distance-travelled graph slope down? Explain.
Show worked answer
No. Already travelled distance cannot be undone. A downward section can instead show decreasing distance from a fixed place.
8
Meeting point
2 marks
Two travellers on the same straight route have distance-from-home graphs meeting at (2, 8). Interpret this.
Show worked answer
They are both 8 km from home after 2 hours, so are at the same point at that time.
9
Curve interpretation
2 marks
A total-distance graph gets steadily steeper. What happens to speed?
Show worked answer
The distance gained in each equal time interval increases, so the traveller speeds up.
10
Instantaneous rate
Higher only3 marks
A tangent at a point on a distance–time curve passes through (2 s, 4 m) and (6 s, 16 m). Estimate the speed there.
Show worked answer
A tangent follows the curve's direction at that instant.
v≈(16−4)/(6−2)=3 m/s
Use points on the tangent, not a chord.
Examiner-style feedback
Common distance–time graphs mistakes
Using the final coordinates
For a section, subtract both starting readings before dividing.
Reading steepness without the scale
Calculate from the numbers and units; apparent angles can mislead.
Confusing distance travelled with distance from home
Read the vertical label before interpreting a descending line.
30-second recap
Choose, carry out, check
Translate the wording before you reach for a rule.
Interpret axis labels.
Separate motion and rests.
Use changes for gradients.
Include rests in overall average speed.
Quick answers
Distance–time graphs FAQ
Is a downward line negative speed?
No. On a straight-route distance-from-home graph it means returning; speed is the magnitude of the rate.
Are tangent estimates Higher?
Estimating instantaneous rates using tangents is Higher content, labelled on the relevant question.
A14/R14 journey graphs across tiers; A15/R15 tangent extension explicitly Higher. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.
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