A man covers three equal distances with the speeds of 10 km/hr, 20 km/hr, and…
2026
A man covers three equal distances with the speeds of 10 km/hr, 20 km/hr, and 30 km/hr respectively. Find his average speed for the whole journey.
- A.
16.36 km/h
- B.
19 km/h
- C.
16.6 km/h
- D.
50 km/h
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Correct answer: A
Key idea: For equal distances, the average speed is the harmonic mean of the speeds (or compute total distance divided by total time).
Let the distance of each leg be d. Total distance = 3d.
Time for each leg = d/10, d/20, d/30. Total time = d/10 + d/20 + d/30 = d*(1/10 + 1/20 + 1/30).
Compute the sum: 1/10 + 1/20 + 1/30 = 6/60 + 3/60 + 2/60 = 11/60, so total time = 11d/60.
Average speed = total distance / total time = (3d) / (11d/60) = 3d * 60 / (11d) = 180/11 ≈ 16.36 km/h.
Answer: 16.36 km/h (exact value 180/11 km/h).
Shortcut: For equal distances use the harmonic mean formula: average speed = n / (sum of reciprocals of the speeds), where n is the number of equal legs.