Discussion
A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
Answer: A
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
Equal times over 4 km downstream and 3 km upstream give the speed ratio:
\[ \frac{4}{b + r} = \frac{3}{b - r} \quad\Longrightarrow\quad 4b - 4r = 3b + 3r \]
\[ b = 7r \quad\Longrightarrow\quad b + r = 8r, \qquad b - r = 6r \]
Now use the 48 km round trip in 14 hours:
\[ \frac{48}{8r} + \frac{48}{6r} = 14 \quad\Longrightarrow\quad \frac{6}{r} + \frac{8}{r} = 14 \]
\[ \frac{14}{r} = 14 \quad\Longrightarrow\quad r = 1 \text{ km/h} \]
So the boat does 7 km/h in still water: 8 km/h downstream for 6 hours and 6 km/h upstream for 8 hours.
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