Discussion
A man goes to Mumbai from Pune at a speed of 4 km/hr and returns to Pune at speed of 6km/hr. What is his average speed of the entire journey?
Answer: A
Average speed is total distance over total time, which for two equal legs is the harmonic mean, not the arithmetic one:
\[ \bar{v} = \frac{2v_{1}v_{2}}{v_{1} + v_{2}} \]
\[ \bar{v} = \frac{2 \times 4 \times 6}{4 + 6} = \frac{48}{10} = 4.8 \text{ km/hr} \]
The arithmetic mean of 5 km/hr is too high, because more time is spent on the slow leg - the average always falls below it.
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