Multiple choice general knowledge math & puzzles

If a boy goes school at 6.8 km/hr and returns home at 4.2 km/hr,find his average speed

  1. 4.9

  2. 5.2

  3. 4.19

  4. 5.19
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When traveling equal distances at different speeds, the average speed is the harmonic mean, not the arithmetic mean. For two speeds, average speed = 2ab/(a+b) = 2(6.8)(4.2)/(6.8+4.2) = 57.12/11 = 5.19 km/hr. Option C (4.19) is the arithmetic mean, which is incorrect for this scenario.

AI explanation

When the same distance is covered at two different speeds (here 6.8 km/hr going, 4.2 km/hr returning), the average speed for the round trip is the harmonic mean, not the simple average: Avg = 2ab/(a+b) = 2×6.8×4.2/(6.8+4.2) = 57.12/11 ≈ 5.19 km/hr. Simply averaging 6.8 and 4.2 (which would give 5.5) is a common mistake, since more time is spent traveling at the slower speed, pulling the true average down toward it -- 5.19 correctly reflects that.

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