Discussion
Surendra covers a distance by cycle at 18 km/h. He returns to the starting point in a bus at a speed of 45 km/h. Find the average speed for the entire journey.
Answer: B
Average speed is total distance over total time, which for two equal legs is the harmonic mean, not the arithmetic one:
\[ \bar{v} = \frac{2v_{1}v_{2}}{v_{1} + v_{2}} \]
\[ \bar{v} = \frac{2 \times 18 \times 45}{18 + 45} = \frac{1620}{63} = 25.71 \text{ km/hr} \]
The arithmetic mean of 31.5 km/hr overstates it, because the slower cycle leg takes far longer than the bus leg and so weighs more heavily in the total time.
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