A car travels 60 km in 2 hours. What is its speed?
Speed = distance ÷ time.
Speed = 60 ÷ 2 = 30 km/h.
Speed, Distance and Time
Speed, distance and time are linked by a simple formula used to describe motion. Speed is a type of compound measure, and accurate calculations often require careful use of units and conversions in real-world problem solving.
Overview
Speed, distance and time are linked by one important formula.
If you know any two of the three values, you can work out the missing one.
\( \text{Speed} = \dfrac{\text{Distance}}{\text{Time}} \)
What you should understand after this topic
- Understand how speed, distance and time are connected
- Choose the correct formula for each question
- Convert units correctly
- Solve journey questions step by step
- Avoid common exam mistakes
Speed
\( s = \dfrac{d}{t} \)
Distance
\( d = s \times t \)
Time
\( t = \dfrac{d}{s} \)
Key Definitions
Speed
How fast something is moving.
Distance
How far something travels.
Time
How long the journey takes.
Average Speed
Total distance divided by total time.
\(\text{km/h}\)
Kilometres travelled in one hour.
\(\text{m/s}\)
Metres travelled in one second.
Key Rules
Use matching units
Do not mix km with metres or hours with seconds.
Speed formula
\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)
Distance formula
\( \text{Distance} = \text{Speed} \times \text{Time} \)
Time formula
\( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \)
Common Units
1 km
\(1000\) metres
1 hour
\(60\) minutes
1 minute
\(60\) seconds
Hours to minutes
Multiply by \(60\)
Minutes to hours
Divide by \(60\)
km/h to m/s
Convert both distance and time units first.
How to Solve
Step 1: Understand speed, distance and time
Speed tells you how much distance is travelled in a given time. It is a type of compound measure.
\( \text{Speed} = \dfrac{\text{Distance}}{\text{Time}} \)
Exam tip: Speed is a rate, so units matter.
Step 2: Choose the correct formula
Find speed
\( \text{speed} = \frac{\text{distance}}{\text{time}} \)
Find distance
\( \text{distance} = \text{speed} \times \text{time} \)
Find time
\( \text{time} = \frac{\text{distance}}{\text{speed}} \)
Average speed
\( \frac{\text{total distance}}{\text{total time}} \)
Step 3: Check units before calculating
Distance and time units must match the speed unit.
For km/h, use kilometres and hours.
For m/s, use metres and seconds.
Exam tip: Convert units before substituting using units and conversions.
Step 4: Average speed
Average speed uses the total distance and total time for the whole journey.
\( \text{Average speed} = \dfrac{\text{total distance}}{\text{total time}} \)
Do not average the separate speeds unless the times are equal.
Step 5: Exam method summary
See compound measures for more rate questions.
- Identify what the question asks for.
- Choose the correct formula.
- Convert units if needed.
- Substitute values carefully.
- Write the answer with correct units.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on calculating speed, distance, and time using standard units.
Edexcel
A car travels 150 km in 3 hours. Calculate its average speed.
Edexcel
A cyclist travels at a speed of 12 km/h for 2.5 hours. Find the distance travelled.
Edexcel
A train travels 360 km at a constant speed of 90 km/h. Calculate the time taken.
Edexcel
A runner completes 800 metres in 200 seconds. Calculate the average speed in m/s.
Edexcel
A car travels 120 km in 1.5 hours. Find its average speed.
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, emphasising unit conversions and multi-step problems.
AQA
A car travels 90 km in 1 hour 30 minutes. Calculate its average speed in km/h.
AQA
A bus travels at 72 km/h for 40 minutes. Find the distance travelled.
AQA
A person walks 2.4 km in 30 minutes. Calculate the speed in km/h.
AQA
Convert 20 m/s to km/h.
AQA
Explain why time must be converted into consistent units when calculating speed.
OCR
Exam-style questions aligned with OCR GCSE Mathematics, focusing on reasoning, compound measures, and real-life applications.
OCR
A plane travels 1,200 km in 2.5 hours. Calculate its average speed.
OCR
A car travels at an average speed of 25 m/s for 3 minutes. Find the distance travelled in metres.
OCR
Two towns are 270 km apart. A car travels at 90 km/h. How long does the journey take?
OCR
A cyclist travels 15 km at 10 km/h and then 15 km at 30 km/h. Calculate the average speed for the entire journey.
OCR
Describe the steps needed to solve problems involving speed, distance, and time.
Exam Checklist
Step 1
Underline what you need to find: speed, distance or time.
Step 2
Choose the correct formula before calculating.
Step 3
Check that all units match.
Step 4
Write the final answer with units.
Most common exam mistakes
Wrong unit conversion
Forgetting that \(30\) minutes is \(0.5\) hours, not \(0.3\) hours.
Wrong formula
Multiplying when you should divide, or dividing when you should multiply.
Average speed mistake
Using one part of the journey instead of total distance and total time.
No unit
Always state km/h, m/s, km, m, hours, minutes or seconds correctly.
Common Mistakes
These are common mistakes students make when working with speed, distance and time in GCSE Maths.
Using the wrong formula
Incorrect
A student uses an incorrect relationship between speed, distance and time.
Correct
Remember the triangle: speed = distance ÷ time, distance = speed × time, time = distance ÷ speed.
Not converting time correctly
Incorrect
A student leaves time in minutes when the speed is in km/h.
Correct
Convert time into the correct units before calculating. For example, 30 minutes = 0.5 hours.
Mixing units
Incorrect
A student combines kilometres with metres or hours with seconds.
Correct
Make sure all units match before using the formula. Convert distances and times into consistent units.
Missing units in the answer
Incorrect
A student gives a numerical answer without units.
Correct
Always include units such as km/h, m/s, km, or hours in your final answer.
Using only part of the journey
Incorrect
A student calculates average speed using only one section of a journey.
Correct
For average speed, use total distance divided by total time across the entire journey.
Try It Yourself
Practise solving problems involving speed, distance and time.
Foundation
Foundation Practice
Use the basic speed, distance and time formulas.
A cyclist travels 45 km in 3 hours. Find the speed in km/h.
Divide distance by time.
45 ÷ 3 = 15 km/h.
A train travels at 80 km/h for 2 hours. How far does it travel?
Distance = speed × time.
Distance = 80 × 2 = 160 km.
A car travels at 50 mph for 4 hours. Find the distance travelled.
Multiply speed by time.
Distance = 50 × 4 = 200 miles.
A runner travels 12 km at 6 km/h. How long does it take?
Time = distance ÷ speed.
Time = 12 ÷ 6 = 2 hours.
A journey is 90 km. The speed is 30 km/h. How many hours does it take?
Time = distance ÷ speed.
90 ÷ 30 = 3 hours.
Which formula finds speed?
Speed means distance per unit of time.
Speed = distance ÷ time.
A bus travels 100 km in 2.5 hours. Find its speed in km/h.
Divide 100 by 2.5.
100 ÷ 2.5 = 40 km/h.
A student calculates speed by doing time ÷ distance. What is wrong?
Speed uses distance first.
Speed = distance ÷ time, not time ÷ distance.
A car travels at 70 km/h for 3 hours. Find the distance travelled.
Distance = speed × time.
70 × 3 = 210 km.
Higher
Higher Practice
Solve speed, distance and time problems involving unit conversion and multi-step reasoning.
A car travels 150 km in 2 hours 30 minutes. What is its average speed?
Convert 2 hours 30 minutes to 2.5 hours.
2 hours 30 minutes = 2.5 hours. Speed = 150 ÷ 2.5 = 60 km/h.
A train travels 180 km in 1 hour 30 minutes. Find its average speed in km/h.
1 hour 30 minutes = 1.5 hours.
Speed = 180 ÷ 1.5 = 120 km/h.
A cyclist travels at 18 km/h for 40 minutes. How far do they travel?
40 minutes = 2/3 of an hour.
Distance = 18 × 2/3 = 12 km.
A car travels at 48 km/h for 15 minutes. Find the distance travelled in km.
15 minutes = 0.25 hours.
Distance = 48 × 0.25 = 12 km.
A journey is 75 miles. A car travels at 50 mph. How long does the journey take?
Time = distance ÷ speed.
75 ÷ 50 = 1.5 hours.
A runner completes 10 km in 50 minutes. Find their average speed in km/h.
50 minutes = 5/6 of an hour.
Speed = 10 ÷ 5/6 = 12 km/h.
A student uses 30 minutes as 0.3 hours. What is wrong?
30 minutes is half an hour.
30 minutes = 30 ÷ 60 = 0.5 hours.
A car travels 135 km at 90 km/h. How many minutes does the journey take?
Find time in hours first, then convert to minutes.
Time = 135 ÷ 90 = 1.5 hours = 90 minutes.
A train travels 60 km at 120 km/h. How long does it take?
60 is half of 120.
Time = 60 ÷ 120 = 0.5 hours = 30 minutes.
A cyclist travels 24 km at 16 km/h. Give the time in hours.
Time = distance ÷ speed.
24 ÷ 16 = 1.5 hours.
Games
Practise this topic with interactive games.
Games coming soon.