Discussion

A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. How far is the place?

Answer: B

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

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

\[ b + r = 7.2 \text{ kmph}, \qquad b - r = 4.8 \text{ kmph} \]

\[ \frac{D}{7.2} + \frac{D}{4.8} = 1 \]

\[ D\left(\frac{1}{7.2} + \frac{1}{4.8}\right) = D\left(\frac{2 + 3}{14.4}\right) = 1 \]

\[ \frac{5D}{14.4} = 1 \quad\Longrightarrow\quad D = 2.88 \text{ km} \]

Using the still-water speed of 6 kmph for both legs would give 3 km - the current always costs time overall, so the real distance is a little less.

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