A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. What is his average speed for the entire journey?

Question

A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. What is his average speed for the entire journey?

1. A. 4 km/h (Correct answer)
2. B. 4.5 km/h
3. C. 5.22 km/h
4. D. 4.87 km/h

Correct Answer

Option A — 4 km/h

Detailed Solution & Explanation

The correct answer is 4 km/h.

Key Points

• When equal distances are covered at two different speeds, the average speed is their harmonic mean:
• Average speed = 2ab ÷ (a + b), where a and b are the two speeds.
• Here a = 6 km/h and b = 3 km/h:
• Average speed = (2 × 6 × 3) ÷ (6 + 3) = 36 ÷ 9 = 4 km/h.
• Why harmonic mean? More time is spent on the slower half, so the average is pulled below the arithmetic mean (which would wrongly give 4.5).
• This is the single most common trap in speed questions.
• use harmonic mean (2ab/(a+b)) for equal distances at two speeds, but the ordinary weighted mean when the times are equal.

Exam Tip

• memorise 2ab/(a+b) for the equal-distance case — it appears in almost every JKSSB and SSC quantitative paper.