Discussion
A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Answer: B
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b + r = 6 \text{ kmph}, \qquad b - r = 3 \text{ kmph} \]
Average speed is total distance over total time, which is the harmonic mean of the two speeds:
\[ \bar{v} = \frac{2 \times 6 \times 3}{6 + 3} = \frac{36}{9} = 4 \text{ kmph} \]
The arithmetic mean would be 4.5 - the still-water speed - but more time is spent on the slow upstream leg, so the true average falls below it. A round trip in a current is always slower on average than the same trip in still water.
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