Discussion

A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?

Answer: D

With \( b \) the still-water speed and \( r \) the stream's,

\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]

Twice the time means half the speed over the same distance:

\[ \frac{b + r}{b - r} = 2 \quad\Longrightarrow\quad 4.5 + r = 2(4.5 - r) = 9 - 2r \]

\[ 3r = 4.5 \quad\Longrightarrow\quad r = 1.5 \text{ km/h} \]

Checking: 6 km/h downstream and 3 km/h upstream. In general \( r = \tfrac{b}{3} \) whenever the upstream leg takes twice as long.

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