GCSE Maths · Ratio, proportion and rates of change

Speed, distance and time GCSE Questions and Worked Answers

Average speed is total distance divided by total time. Use consistent units; at constant speed, distance is speed × time and time is distance ÷ speed.

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Start with the meaning

What you need to know about speed, distance and time

A cyclist travels 36 kilometres in 3 hours. If that distance were spread evenly over the time, there would be 12 kilometres in each hour. We call this an average speed of 12 kilometres per hour, written 12 km/h. The cyclist need not actually ride at 12 km/h throughout.

See the idea first

A rate tells you how much distance goes with one time unit

At a constant speed, doubling the time doubles the distance. Write d for distance, t for time and v for speed. The relationship is d = vt, so dividing by time gives v = d ÷ t and dividing by speed gives t = d ÷ v.

Travelling at a constant 12 km/h
Time (h)	Distance (km)	Reason
1	12	12 km in one hour
2	24	twice as long
0.5	6	half an hour

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.

Find a speed

What the problem asks: A runner covers 600 m in 150 s. Find average speed.

How to solve it: 600 ÷ 150 = 4 m/s. The units follow the distance and time used.

Find a travel time

What the problem asks: How long does 84 km take at a constant 56 km/h?

How to solve it: 84 ÷ 56 = 1.5 hours, or 1 hour 30 minutes. Half an hour is 30 minutes, not 50.

Average a whole journey

What the problem asks: A car covers 60 km in one hour and another 60 km in two hours. Find its average speed.

How to solve it: Total distance is 120 km and total time is 3 hours, so average speed is 40 km/h. The ordinary mean of 60 and 30 is not appropriate because the times differ.

A reliable routine

Use two quantities to find the third

For constant-speed motion, or a whole journey with an average speed, distance equals the rate multiplied by elapsed time. Choose the rearrangement that answers the question; no formula triangle is needed to understand it.

Write the distance, time and speed you know, with units.
Convert the units before calculating: minutes ÷ 60 gives hours.
Use distance ÷ time, speed × time, or distance ÷ speed as appropriate.
For a whole journey, include every leg and any stops specified. Interpret fractional hours as minutes.

Check: 1 hour 20 minutes is 1 + 20/60 hours, not 1.20 hours. Average speed uses elapsed time if stops are included in the journey.

Fully worked

Speed, distance and time GCSE worked examples

Each solution explains the clue, why the method fits and how to check the result.

Example 1

Average speed

2 marks

Question

A train covers 154 km in 2 hours. Find its average speed.

v=\frac{154}{2}=77\text{ km/h}

The distance per hour is 77 km on average.

Example 2

Find distance

2 marks

Question

A car travels at a constant 72 km/h for 45 minutes. Find the distance.

Convert first:

t=\frac{45}{60}=0.75\text{ h}

d=72(0.75)=54\text{ km}

Tip: do not multiply 72 by 45 when the rate is per hour.

Example 3

Find time

3 marks

Question

A cyclist covers 42 km at an average speed of 24 km/h. Give the time in hours and minutes.

t=\frac{42}{24}=1.75\text{ h}

The fractional hour is 0.75 × 60 = 45 minutes. Time: 1 hour 45 minutes.

Example 4

Convert a rate

3 marks

Question

Convert 54 km/h to m/s.

54 km is 54,000 m; one hour is 3,600 s.

\frac{54000}{3600}=15\text{ m/s}

This explains the shortcut of dividing km/h by 3.6.

Example 5

Average unequal times

4 marks

Question

A driver travels 90 km in 1.5 hours, then 60 km in 2 hours, including all stops. Find the whole-journey average speed to one decimal place.

d_{\rm total}=90+60=150\text{ km}

t_{\rm total}=1.5+2=3.5\text{ h}

v_{\rm average}=\frac{150}{3.5}=42.857\ldots\text{ km/h}

The average speed is 42.9 km/h to one decimal place. The stage speeds are 60 and 30 km/h, but averaging those gives 45 km/h: that is wrong because the driver spends longer at the slower speed.

Example 6

Arrival after a stop

4 marks

Question

A coach leaves at 09:25. It travels 120 km at 60 km/h, stops for 25 minutes, then travels 45 km at 45 km/h. When does it arrive?

First leg: $120/60=2$ hours. Second leg: $45/45=1$ hour. Total elapsed time is 3 hours 25 minutes. 09:25 + 3 hours = 12:25, then + 25 minutes = 12:50. Include the stationary time.

10 original questions · total 24 marks

Speed, distance and time GCSE exam-style questions

Try each question before opening its fully worked answer. The difficulty rises through the set.

Before you startAllow about 29 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed

Metres per second

2 marks

A runner travels 350 m in 70 s. Find average speed.

Show worked answer

v=350/70=5\text{ m/s}

Divide distance by time.

Distance

2 marks

Find the distance travelled at 18 m/s for 25 s.

Show worked answer

d=18\times25=450\text{ m}

Seconds cancel the ‘per second’ unit.

Minutes to hours

2 marks

A car travels at 48 km/h for 35 minutes. Find the distance.

Show worked answer

t=\frac{35}{60}\text{ h}

d=48\times\frac{35}{60}=28\text{ km}

Time in minutes

2 marks

How long does a 15 km ride take at 20 km/h?

Show worked answer

t=15/20=0.75\text{ h}

0.75\times60=45\text{ minutes}

Convert to km/h

2 marks

Convert 8 m/s to km/h.

Show worked answer

In one hour, distance is $8\times3600=28800$ m = 28.8 km. Speed is 28.8 km/h.

Average with a stop

3 marks

A walker covers 8 km in 2 hours of walking and takes a 30-minute rest. Find average speed over the complete outing.

Show worked answer

Elapsed time is $2+30/60=2.5$ h.

v=8/2.5=3.2\text{ km/h}

Include the rest because the complete outing is requested.

Equal distances, different times

3 marks

Travel 40 km at 40 km/h and return 40 km at 20 km/h. Find the average speed to one decimal place.

Show worked answer

Times are $40/40=1$ h and $40/20=2$ h.

v=\frac{80}{3}=26.666\ldots

Average speed is 26.7 km/h, not 30.

Compare

3 marks

Runner A covers 200 m in 25 s. Runner B covers 300 m in 40 s. Who has the greater average speed?

Show worked answer

A: $200/25=8$ m/s. B: $300/40=7.5$ m/s. A is faster; comparing distances alone would mislead.

Meeting a deadline

3 marks

A van must cover 105 km in 1 hour 30 minutes. What average speed is required?

Show worked answer

Time is $1+30/60=1.5$ h.

v=105/1.5=70\text{ km/h}

This is a mathematical average, not advice to exceed road limits.

Correct a time conversion

2 marks

A student writes 2 hours 15 minutes as 2.15 hours. Correct it and explain.

Show worked answer

A minute is 1/60 of an hour.

2+\frac{15}{60}=2.25\text{ hours}

0.15 hours would be only 9 minutes.

Examiner-style feedback

Common speed, distance and time mistakes

Minutes treated as hundredths

Convert through 60, not 100.

Averaging speeds without time weights

Add distances and times separately, then divide their totals.

Leaving out units

12 m/s and 12 km/h are very different rates.

30-second recap

Choose, carry out, check

Translate the wording before you reach for a rule.

Match units.
Identify the unknown.
Use distance = speed × time.
Average a journey from totals.

Quick answers

Speed, distance and time FAQ

Does average speed mean constant speed?

No. It is the constant speed that would cover the total distance in the same elapsed time.

Do stops count?

Yes when the whole journey or elapsed time is requested; follow the wording if moving time is specified instead.

Build connected skills

What to revise next

See motion

Velocity–time graphs

Connect rate, gradient and distance.

Revise velocity–time graphs

Uncertain measurements

Upper and lower bounds

Find possible limits for a calculated rate.

Revise upper and lower bounds

Content standards

Curriculum and rights review

R1/R11 compound units, constant and average speed across tiers; no differential calculus. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.

Official specification references

AQA GCSE Maths subject content