Speed, distance and time | OCR GCSE Maths Notes

Visual model

Speed, distance and time triangle

distancespeedtimecover the one you need

Gold-standard guide

20 mins

What you will learn

Use rate formulae and convert units correctly.

Use a clear step-by-step method for speed, distance and time.

Check your answer and avoid the most common exam mistake.

Useful before you start

Core number skillsEarlier ratio, proportion and rates of change skillsShowing clear working

Core knowledge

Know the rule, then use it

These are the short notes. Read each one, then check you can use it in the worked example below.

Method

Speed, distance and time form a triangle: cover what you want to find

Step 1

Find the time for the cyclist

Time = distance/speed = $7\frac{5}{2}5$ = 3 hours

Step 2

Find the train's speed in km/h

Speed = $18\frac{0}{2}$ .5 = 72 km/h

Step 3

Convert 72 km/h to m/s

Multiply by 1000 (km to m) then divide by 3600 (hours to seconds): 72 × $100\frac{0}{3}600$ = 20 m/s

Watch out

Students confuse the conversion factor

Speed

$speed = distanc\frac{e}{time}.$

Distance

$distance = speed \times time.$

Worked example

A cyclist rides 75 km at an average speed of 25 km/h. How long does the journey take? Then, a train takes 2.5 hours to travel 180 km. Find its speed in m/s.

Find the time for the cyclist: Time = distance/speed = $7\frac{5}{2}5$ = 3 hours.

Find the train's speed in km/h: Speed = $18\frac{0}{2}$ .5 = 72 km/h.

Convert 72 km/h to m/s: Multiply by 1000 (km to m) then divide by 3600 (hours to seconds): 72 × $100\frac{0}{3}600$ = 20 m/s.

Final answer

Cyclist time = 3 hours; train speed = 20 m/s

Question ladder

Build up to the hardest questions

Do them in order. If you miss a step, read the solution, then redo the question without looking.

Workedreasoning

A cyclist rides 75 km at an average speed of 25 km/h. How long does the journey take? Then, a train takes 2.5 hours to travel 180 km. Find its speed in m/s.

3 marks4 minsspeed-distance-and-time-worked

Show solution

Worked solution

1.Find the time for the cyclist: Time = distance/speed = $7\frac{5}{2}5$ = 3 hours.
2.Find the train's speed in km/h: Speed = $18\frac{0}{2}$ .5 = 72 km/h.
3.Convert 72 km/h to m/s: Multiply by 1000 (km to m) then divide by 3600 (hours to seconds): 72 × $100\frac{0}{3}600$ = 20 m/s.

Final answer

Cyclist time = 3 hours; train speed = 20 m/s

Mark points

M1: find the time for the cyclist
M1: find the train's speed in km/h
M1: convert 72 km/h to m/s
A1: Cyclist time = 3 hours; train speed = 20 m/s

Watch out

Students confuse the conversion factor. 6. 6.Write these conversion factors at the top of any question involving unit changes.

Diagnosticrecall

A car travels 240 km in 3 hours. Find its speed in km/h.

1 mark2 minsspeed-distance-and-time-q1

Show solution

Worked solution

1.Spot the skill: Speed, distance and time form a triangle: cover what you want to find.
2.Use the find the time for the cyclist stage first, then find the train's speed in km/h.
3.Keep the final answer visible: 80 km/h.

Final answer

80 km/h

Mark points

M1: use the correct speed, distance and time form a triangle: cover what you want to find. speed = distance/time.distance = speed × time. time = distance/speed. always convert units before substituting.
A1: 80 km/h

Watch out

Students confuse the conversion factor. 6. 6.Write these conversion factors at the top of any question involving unit changes.

Easyprocedure

Convert 90 km/h to m/s.

2 marks3 minsspeed-distance-and-time-q2

Show solution

Worked solution

1.Spot the skill: Speed, distance and time form a triangle: cover what you want to find.
2.Use the find the train's speed in km/h stage first, then convert 72 km/h to m/s.
3.Keep the final answer visible: 25 m/s.

Final answer

25 m/s

Mark points

M1: use the correct speed, distance and time form a triangle: cover what you want to find. speed = distance/time.distance = speed × time. time = distance/speed. always convert units before substituting.
A1: 25 m/s

Watch out

Students confuse the conversion factor. 6. 6.Write these conversion factors at the top of any question involving unit changes.

Mediumreasoning

A jogger runs at 8 km/h for 45 minutes. How far do they run?

3 marks4 minsspeed-distance-and-time-q3

Show solution

Worked solution

1.Spot the skill: Speed, distance and time form a triangle: cover what you want to find.
2.Use the convert 72 km/h to m/s stage first, then find the time for the cyclist.
3.Keep the final answer visible: 6 km.

Final answer

6 km

Mark points

M1: use the correct speed, distance and time form a triangle: cover what you want to find. speed = distance/time.distance = speed × time. time = distance/speed. always convert units before substituting.
A1: 6 km

Watch out

Students confuse the conversion factor. 6. 6.Write these conversion factors at the top of any question involving unit changes.

Hardproblem solving

Train A takes 2 h to cover 160 km. Train B covers 300 km in 3.5 h. Which is faster?

3 marks5 minsspeed-distance-and-time-q4

Show solution

Worked solution

1.Spot the skill: Speed, distance and time form a triangle: cover what you want to find.
2.Use the find the time for the cyclist stage first, then find the train's speed in km/h.
3.Keep the final answer visible: Train A at 80 km/h; Train B at 85.7 km/h — Train B is faster.

Final answer

Train A at 80 km/h; Train B at 85.7 km/h — Train B is faster

Mark points

M1: use the correct speed, distance and time form a triangle: cover what you want to find. speed = distance/time.distance = speed × time. time = distance/speed. always convert units before substituting.
A1: Train A at 80 km/h; Train B at 85.7 km/h — Train B is faster

Watch out

Students confuse the conversion factor. 6. 6.Write these conversion factors at the top of any question involving unit changes.

Exam-stylemulti-step

A round trip covers 400 km. The outward leg takes 4 h, the return 6 h. Find the average speed.

4 marks6 minsspeed-distance-and-time-q5

Show solution

Worked solution

1.Spot the skill: Speed, distance and time form a triangle: cover what you want to find.
2.Use the find the train's speed in km/h stage first, then convert 72 km/h to m/s.
3.Keep the final answer visible: 40 km/h.

Final answer

40 km/h

Mark points

M1: use the correct speed, distance and time form a triangle: cover what you want to find. speed = distance/time.distance = speed × time. time = distance/speed. always convert units before substituting.
A1: 40 km/h

Watch out

Students confuse the conversion factor. 6. 6.Write these conversion factors at the top of any question involving unit changes.

Grade 9 stretchproblem solving

A car travels 120 km at 60 km/h and then 120 km at 80 km/h. Find its average speed for the whole journey.

4 marks7 minsspeed-g9

Show solution

Worked solution

1.Find each journey time.
2.Add the times and distances.
3.Divide total distance by total time.

Final answer

68.6 km/h to 3 significant figures

Mark points

M1: times 2 and 1.5 hours
M1: use 240 / 3.5
A1: 68.6 km/h

Watch out

Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.

Timed checkpoint

12 mins - 9 marks

Switch between skills

Set a timer and attempt all four questions before opening any answers. This is closer to the way skills appear in a real paper.

1Speed, distance and time - 2 marksA car travels 240 km in 3 hours. Find its speed in km/h.Mark answer

Answer

80 km/h

2Ratio and sharing - 2 marksTwo people share profit in ratio 5:3. Total profit £640. Find each share.Mark answer

Answer

£400 and £240

3Fractions and ratios - 2 marksA map scale is 1:25,000. Express as a fraction.Mark answer

Answer

$\frac{1}{2}5$ ,000

4Direct and inverse proportion - 3 marksy ∝ 1/x². When x = 2, y = 9. Find y when x = 6.Mark answer

Answer

Mastery check

I can explain the method for speed, distance and time.
I can show clear working without skipping key steps.
I can avoid this mistake: Students confuse the conversion factor. 6. 6.Write these conversion factors at the top of any question involving unit changes.

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