A man pedals a cycle from his house to his office at a speed of 10 km/h and back from the office to his house at a speed of 15 km/h. His average speed (in km/h) is:
12
For equal distances at two different speeds, average speed is the harmonic mean of the speeds, not the arithmetic mean.
\[v_{avg} = \frac{2 v_1 v_2}{v_1 + v_2} = \frac{2 \times 10 \times 15}{10 + 15} = \frac{300}{25} = 12 \text{ km/h}\]
The cyclist spends more time at the slower 10 km/h leg than at the 15 km/h leg, so the average (12) is below the arithmetic mean (12.5). Answer: 12 km/h.
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