Sec 1 Maths · Ratio, rate and speed

Distance–time graphs questions with answers

Practice questions on distance–time graphs, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

The distance–time graph shows Devi's cycle ride from home. Find Devi's distance, in km, from home 30 minutes after setting off.

Step 1 of 1

Go up from 30 min on the time axis to the graph, then across to the distance axis

30 minutes after setting off, the graph is at

10

km.

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Questions

Question 1Read a distance or a time off the graph
The distance–time graph shows Devi's walk from home. Find Devi's distance, in km, from home at 0720.
Show the worked solution
1. Step 1: Go up from 0720 on the time axis to the graph, then across to the distance axisAt 0720, the graph is at $1$ km.
Question 2The speed of one stage (the gradient)
The distance–time graph shows Mei Ling's run from the start. Find Mei Ling's speed from B to C, in m/s.
Show the worked solution
1. Step 1: Read the distances at B and C: the distance travelled (the rise) $\text{Distance} = 480 - 240$ $\phantom{\text{Distance}} = 240 \text{ m}$
2. Step 2: Read the times at B and C: the time taken (the run) $\text{Time taken} = 200 - 120$ $\phantom{\text{Time taken}} = 80 \text{ s}$
3. Step 3: Speed = distance ÷ time $\text{Speed} = \dfrac{240}{80}$ $\phantom{\text{Speed}} = 3 \text{ m/s}$
Question 3How long a stop lasted (a flat stage)
The distance–time graph shows Ali's drive from Town P. Ali stopped once on the way. Find the length of time, in minutes, for which Ali stopped.
Show the worked solution
1. Step 1: A flat stage: the distance doesn't change, so it is the stopThe flat stage is AB.
2. Step 2: Read the times at A and BFrom 0930 to 1000: $30$ min
Question 4Which stage was fastest
The distance–time graph shows Mei Ling's run from the start. State the stage of the journey on which Mei Ling was moving fastest.
Show the worked solution
1. Step 1: Each moving stage's speed: distance ÷ time $\text{OA}: \dfrac{40}{10} = 4 \text{ m/s}$ $\text{AB}: \dfrac{280}{50} = 5.6 \text{ m/s}$ $\text{BC}: \dfrac{280}{80} = 3.5 \text{ m/s}$
2. Step 2: The fastest stage is the steepest oneThe fastest stage is AB: it is the steepest.
Question 5Average speed for the whole journey
The distance–time graph shows Chen Wei's cycle ride from home. Find Chen Wei's average speed for the whole journey, in km/h.
Show the worked solution
1. Step 1: Total distance travelledThe journey ends $38$ km from home.
2. Step 2: Total time, from the start to the end (stops included)From $0$ to $160$ min: $160$ min
3. Step 3: Average speed = total distance ÷ total time (in hours) $\text{Average speed} = 38 \div \dfrac{160}{60}$ $\phantom{\text{Average speed}} = 14.25 \text{ km/h}$
Question 6There and back: the way home
The distance–time graph shows Farah's drive from Town P and back again. Find Farah's speed on the way back, from C to D, in km/h.
Show the worked solution
1. Step 1: Read the distances at C and D: the distance travelled (the drop)From $160$ km to $0$ km: $160$ km
2. Step 2: Read the times at C and D: the time taken (the run)From 1015 to 1215: $120$ min
3. Step 3: Speed = distance ÷ time, with the time in hours (minutes ÷ 60) $\text{Speed} = 160 \div \dfrac{120}{60}$ $\phantom{\text{Speed}} = 80 \text{ km/h}$
Question 7Two journeys: meeting, arriving first
P and Q are 6 km apart. Ravi walks from P to Q, and Devi walks from Q to P along the same road. The graph shows their journeys. Find the distance, in km, from P at which they meet.
Show the worked solution
1. Step 1: They meet where the two graphs cross: go across from the crossing to the distance axisThe graphs cross at $4$ km from P.

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Worked example

The distance–time graph shows Devi's cycle ride from home. Find Devi's distance, in km, from home 30 minutes after setting off.

Step 1 of 1

Go up from 30 min on the time axis to the graph, then across to the distance axis

30 minutes after setting off, the graph is at

10

km.

Questions

Question 1Read a distance or a time off the graph

The distance–time graph shows Devi's walk from home. Find Devi's distance, in km, from home at 0720.

Show the worked solution

Step 1: Go up from 0720 on the time axis to the graph, then across to the distance axisAt 0720, the graph is at $1$ km.

Question 2The speed of one stage (the gradient)

The distance–time graph shows Mei Ling's run from the start. Find Mei Ling's speed from B to C, in m/s.

Show the worked solution

Step 1: Read the distances at B and C: the distance travelled (the rise) $\text{Distance} = 480 - 240$ $\phantom{\text{Distance}} = 240 \text{ m}$
Step 2: Read the times at B and C: the time taken (the run) $\text{Time taken} = 200 - 120$ $\phantom{\text{Time taken}} = 80 \text{ s}$
Step 3: Speed = distance ÷ time $\text{Speed} = \dfrac{240}{80}$ $\phantom{\text{Speed}} = 3 \text{ m/s}$

Question 3How long a stop lasted (a flat stage)

The distance–time graph shows Ali's drive from Town P. Ali stopped once on the way. Find the length of time, in minutes, for which Ali stopped.

Show the worked solution

Step 1: A flat stage: the distance doesn't change, so it is the stopThe flat stage is AB.
Step 2: Read the times at A and BFrom 0930 to 1000: $30$ min

Question 4Which stage was fastest

The distance–time graph shows Mei Ling's run from the start. State the stage of the journey on which Mei Ling was moving fastest.

Show the worked solution

Step 1: Each moving stage's speed: distance ÷ time $\text{OA}: \dfrac{40}{10} = 4 \text{ m/s}$ $\text{AB}: \dfrac{280}{50} = 5.6 \text{ m/s}$ $\text{BC}: \dfrac{280}{80} = 3.5 \text{ m/s}$
Step 2: The fastest stage is the steepest oneThe fastest stage is AB: it is the steepest.

Question 5Average speed for the whole journey

The distance–time graph shows Chen Wei's cycle ride from home. Find Chen Wei's average speed for the whole journey, in km/h.

Show the worked solution

Step 1: Total distance travelledThe journey ends $38$ km from home.
Step 2: Total time, from the start to the end (stops included)From $0$ to $160$ min: $160$ min
Step 3: Average speed = total distance ÷ total time (in hours) $\text{Average speed} = 38 \div \dfrac{160}{60}$ $\phantom{\text{Average speed}} = 14.25 \text{ km/h}$

Question 6There and back: the way home

The distance–time graph shows Farah's drive from Town P and back again. Find Farah's speed on the way back, from C to D, in km/h.

Show the worked solution

Step 1: Read the distances at C and D: the distance travelled (the drop)From $160$ km to $0$ km: $160$ km
Step 2: Read the times at C and D: the time taken (the run)From 1015 to 1215: $120$ min
Step 3: Speed = distance ÷ time, with the time in hours (minutes ÷ 60) $\text{Speed} = 160 \div \dfrac{120}{60}$ $\phantom{\text{Speed}} = 80 \text{ km/h}$

Question 7Two journeys: meeting, arriving first

P and Q are 6 km apart. Ravi walks from P to Q, and Devi walks from Q to P along the same road. The graph shows their journeys. Find the distance, in km, from P at which they meet.

Show the worked solution

Step 1: They meet where the two graphs cross: go across from the crossing to the distance axisThe graphs cross at $4$ km from P.