A car covers the first 40 km of a journey at a speed of 20 km/h and the next…

Concept

Average speed over a whole journey is defined as total distance divided by total time, not the arithmetic mean of the individual speeds. The arithmetic mean of the speeds is correct only when equal TIME is spent at each speed; when equal DISTANCES are travelled, you must add the distances and add the times separately.

Application

1. First leg: distance = 40 km at 20 km/h, so time = 40 ÷ 20 = 2 h.

2. Second leg: distance = 60 km at 30 km/h, so time = 60 ÷ 30 = 2 h.

3. Total distance = 40 + 60 = 100 km.

4. Total time = 2 + 2 = 4 h.

5. Average speed = total distance ÷ total time = 100 ÷ 4 = 25 km/h.

Cross-check

Here each leg happens to take the same time (2 h each), so the journey is split by equal time. In that special case the time-weighted average of 20 and 30 equals their simple mean, (20 + 30) ÷ 2 = 25 km/h, which confirms the result. Note this agreement is a coincidence of equal times; whenever the times differ, only the total-distance-over-total-time method gives the right value.