Discussion
A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
Answer: B
Equal distances each way call for the harmonic mean, not the arithmetic one.
\[ \bar{v} = \frac{2 \times 20 \times 30}{20 + 30} = \frac{1200}{50} = 24 \text{ kmph} \]
The arithmetic mean of 25 kmph is too high, because more time is spent on the slower outward leg.
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