Discussion
A man travels from A to B at a speed of 30 kmph and returns with a speed of 60 kmph. What is the average speed of the man?
Answer: D
Average speed is total distance over total time, which for two equal legs is the harmonic mean, not the arithmetic one:
\[ \bar{v} = \frac{2v_{1}v_{2}}{v_{1} + v_{2}} \]
\[ \bar{v} = \frac{2 \times 30 \times 60}{30 + 60} = \frac{3600}{90} = 40 \text{ kmph} \]
The arithmetic mean of 45 kmph is the trap; the return trip at double the speed takes half the time, so the slow outward leg dominates.
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