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Speed and rates: total distance, total time and unit conversions

Average speed describes the whole journey. Add the distances and add the elapsed times, including a stop when the question includes it in the journey. Averaging the speeds directly is usually wrong because the stages may take different times.

Choose the method

Use speed = distance/time. Choose a consistent unit pair, such as kilometres and hours or metres and seconds.

Convert minutes to hours by dividing by 60. Convert km/h to m/s by dividing by 3.6. Decimal hours are fractions of an hour: 0.4 hours is 24 minutes.

For a multi-stage journey, a table with distance, speed and time prevents mixing quantities. If two objects move towards each other, add their speeds only after placing them in the same units.

Worked examples

Example 1

A cyclist travels 12 km at 18 km/h, then 8 km at 12 km/h. Find the average speed.

First time = 12/18 = 2/3 hour. Second time = 8/12 = 2/3 hour.
Total distance = 20 km; total time = 4/3 hours.
Average speed = 20 ÷ (4/3) = 15 km/h. Here the arithmetic mean happens to work because the times are equal.

Example 2

A train moving at 72 km/h passes a pole in 9 seconds. Find its length, assuming constant speed.

72 km/h = 72 ÷ 3.6 = 20 m/s.
The whole train travels its own length while passing the pole.
Length = 20 × 9 = 180 m. Passing a platform would require adding the platform length.

Try it yourself

A car travels 60 km at 60 km/h and returns the same distance at 40 km/h. Find its average speed.

Show the worked answer

Total time = 60/60 + 60/40 = 2.5 hours.
Total distance = 120 km. Average speed = 120/2.5 = 48 km/h, not 50 km/h.

Common mistakes

Use elapsed journey time if a rest is included, not just moving time.
Do not read 1.5 hours as 1 hour 5 minutes. It is 1 hour 30 minutes.

Sources and review

SEAB 2026 syllabus: O-Level Mathematics 4052: rate and speed.

Original Rae practice, prepared with AI assistance. Selected numerical results and their displayed working are automatically checked at publication; this does not verify every explanation. Curriculum references checked on 5 September 2026. No teacher review or SEAB endorsement is claimed.

What the syllabus expects

the ideas of average rate and average speed
converting units, for instance from km/h to m/s

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More O-Level Elementary Maths (E-Maths) topics

Whole numbers and the operations performed on them · Ratio and proportion · Percentage · Algebraic expressions and formulae · Functions together with their graphs · Equations and inequalities · all of O-Level Elementary Maths (E-Maths)