Rate and Speed
A rate compares two quantities with different units. Average speed is total distance divided by total time, so convert units before combining parts of a journey. When a question gives distance and time, identify what is being asked and keep the units attached to each value.
What this guide covers
Average rate, average speed and unit conversion, including interpreting rates with consistent units in context.
Syllabus reference: 2026 Mathematics 4052, N4, pages 5–6. These are Mentora search groupings, not new official syllabus categories.
Worked example
A cyclist travels 18 km in 45 minutes. Find the average speed in km/h and m/s.
45 minutes is 0.75 h, so the average speed is 18 ÷ 0.75 = 24 km/h. Since 1 km/h = 5/18 m/s, this is 24 × 5/18 = 6⅔ m/s. The distance and time units must match the requested speed unit.
Average speed over a two-part journey
A van travels 30 km in 40 minutes and then 20 km in 20 minutes. Find its average speed for the whole trip in km/h.
Total distance is 50 km. Total time is 60 minutes = 1 hour. Average speed is 50 ÷ 1 = 50 km/h. Do not take the unweighted mean of the two segment speeds when the times differ.
Try three practice checks
Attempt each on paper before revealing the worked answer. These sample particular skills; they do not diagnose the whole topic or establish mastery.
Check 1
Convert 72 km/h to m/s.
Show worked answer
72 × 5/18 = 20 m/s.
Check 2
A runner covers 900 m in 3 minutes. Find the average speed in m/s.
Show worked answer
3 minutes is 180 seconds. Average speed = 900 ÷ 180 = 5 m/s.
Check 3
A tap fills 12 litres in 4 minutes. What is its average rate in litres per minute?
Show worked answer
12 ÷ 4 = 3 litres per minute. State both the quantity and its unit.
Mistakes to watch for
- Do not divide kilometres by minutes and label the answer km/h; convert one unit first.
- Average speed is total distance divided by total time, not automatically the mean of the speeds on each segment.
- Read the context to identify the requested rate and write its unit in the final answer.
If one of these occurs, compare the relevant step with the worked example, then try a different question before drawing conclusions.
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To understand a recurring error rather than relearn the whole skill: Check the 4052 syllabus and revision order.
Published by Mentora · Sources checked 23 Sept 2026
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Original public examples and answers were checked with automated mathematical/editorial QA. No individual author, human reviewer or independent expert review is recorded.