A car covers a distance at 50 km/h and returns at 40 km/h. What is the average speed for the whole journey?

Question

A car covers a distance at 50 km/h and returns at 40 km/h. What is the average speed for the whole journey?

1. A. 44.4 km/h (Correct answer)
2. B. 46.4 km/h
3. C. 46.8 km/h
4. D. 48.6 km/h

Correct Answer

Option A — 44.4 km/h

Detailed Solution & Explanation

The correct answer is 44.4 km/h.

Key Points

• The car covers the same distance each way at two different speeds, so the average speed is the harmonic mean:
• Average speed = 2ab ÷ (a + b), with a = 50 km/h and b = 40 km/h.
• Average speed = (2 × 50 × 40) ÷ (50 + 40) = 4000 ÷ 90 = 44.44 ≈ 44.4 km/h.
• for equal distances at speeds a and b, the average is not (a + b)/2 = 45; it is the harmonic mean 2ab/(a + b), which is always slightly less because more time is spent at the slower speed on the return trip.

Exam Tip

• the 'goes and returns' phrasing is the signal for equal distances — apply 2ab/(a+b) directly.
• The simple average (45) is always offered as a trap option.