Speed, Distance and Time

Speed, distance and time is one of the most practical topics in the Edexcel GCSE Mathematics (1MA1) specification. It is classified as a compound measure because speed involves two different units (distance and time). Questions appear across all three papers and may include distance-time graphs, unit conversions and multi-step problems.

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Key Vocabulary

Term	Meaning
Speed	How fast something is moving (distance per unit time)
Average speed	Total distance / Total time
Distance	How far something travels
Time	The duration of the journey
Compound measure	A measure involving two different units

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The Speed-Distance-Time Triangle

The three formulae linking speed, distance and time are:

• Speed = Distance / Time ($S = \frac{D}{T}$S=TD​)
• Distance = Speed x Time ($D = S \times T$D=S×T)
• Time = Distance / Speed ($T = \frac{D}{S}$T=SD​)

Formula	Use When You Need To Find
$S = \frac{D}{T}$S=TD​	Speed (given distance and time)
$D = S \times T$D=S×T	Distance (given speed and time)
$T = \frac{D}{S}$T=SD​	Time (given distance and speed)

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Worked Examples

Worked Example 1

A car travels 180 miles in 3 hours. What is its average speed?

• Speed = Distance / Time = 180 / 3 = 60 mph

Worked Example 2

A cyclist rides at 15 km/h for 2.5 hours. How far does the cyclist travel?

• Distance = Speed x Time = 15 x 2.5 = 37.5 km

Worked Example 3

A jogger runs 8 km at an average speed of 10 km/h. How long does it take?

• Time = Distance / Speed = 8 / 10 = 0.8 hours = 48 minutes

Edexcel Exam Tip: On Paper 1 (non-calculator), always convert time to a fraction or a decimal of an hour before dividing. For example, 45 minutes = 3/4 hour = 0.75 hours.

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Converting Time

Time conversions are essential for speed problems.

Conversion	Rule
Minutes to hours	Divide by 60
Hours to minutes	Multiply by 60
Decimal hours to minutes	Multiply the decimal part by 60

Worked Example 4

Convert 2 hours 20 minutes to hours.

• 20 minutes = 20/60 = 1/3 hour
• Total = 2 + 1/3 = 2 hours and 20 minutes = 7/3 hours = 2.333... hours

Worked Example 5

Convert 1.35 hours to hours and minutes.

• 0.35 x 60 = 21 minutes
• Answer: 1 hour 21 minutes

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Converting Speed Units

km/h to m/s

Divide by 3.6 (or multiply by 1000/3600).

m/s to km/h

Multiply by 3.6 (or multiply by 3600/1000).

Worked Example 6

Convert 72 km/h to m/s.

• 72 / 3.6 = 20 m/s

Worked Example 7

Convert 15 m/s to km/h.

• 15 x 3.6 = 54 km/h

mph and km/h

Use the approximation 5 miles = 8 km.

Worked Example 8

Convert 50 mph to km/h (approximately).

• 50 x 8/5 = 80 km/h

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Multi-Step Speed Problems

Worked Example 9

A train leaves London at 09:15 and arrives in Birmingham at 10:45. The distance is 180 km. Calculate the average speed.

1. Journey time = 10:45 - 09:15 = 1 hour 30 minutes = 1.5 hours
2. Speed = 180 / 1.5 = 120 km/h

Worked Example 10

Sarah drives 90 miles at 60 mph, then 40 miles at 40 mph. Find her average speed for the whole journey.

1. Time for first part = 90 / 60 = 1.5 hours
2. Time for second part = 40 / 40 = 1 hour
3. Total distance = 90 + 40 = 130 miles
4. Total time = 1.5 + 1 = 2.5 hours
5. Average speed = 130 / 2.5 = 52 mph

Edexcel Exam Tip: Average speed is not the same as the average of the two speeds! You must calculate total distance / total time. This is a very common mistake.

Worked Example 11

A cyclist rides 24 km at 16 km/h, rests for 30 minutes, then rides 18 km at 12 km/h. Find the average speed for the entire journey (including rest time).

1. Time riding first section = 24 / 16 = 1.5 hours
2. Rest time = 0.5 hours
3. Time riding second section = 18 / 12 = 1.5 hours
4. Total time = 1.5 + 0.5 + 1.5 = 3.5 hours
5. Total distance = 24 + 18 = 42 km
6. Average speed = 42 / 3.5 = 12 km/h

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Distance-Time Graphs

A distance-time graph shows how distance changes over time.

Feature	Meaning
Horizontal line	Object is stationary (not moving)
Straight diagonal line going up	Object is moving at constant speed
Steeper line	Faster speed
Curved line	Changing speed (acceleration or deceleration)
Gradient of the line	Speed (gradient = distance / time)

Worked Example 12

A distance-time graph shows a straight line from (0, 0) to (2, 30). What is the speed?

• Gradient = change in distance / change in time = 30 / 2 = 15 km/h

Worked Example 13

A journey is shown on a distance-time graph: from (0, 0) to (1, 40), then horizontal from (1, 40) to (1.5, 40), then from (1.5, 40) to (3, 0). Describe the journey.

• 0 to 1 hour: travels 40 km at 40 km/h
• 1 to 1.5 hours: stops for 30 minutes
• 1.5 to 3 hours: returns 40 km in 1.5 hours at 40/1.5 = 26.67 km/h (approximately)

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Practice Problems