Discussion
A boat covers a certain distance downstream in 1 hour, while it comes back in 1 1/2 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?
Answer: D
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
The distance is the same both ways, so speeds are inversely proportional to times:
\[ \frac{b + 3}{b - 3} = \frac{1.5}{1} = \frac{3}{2} \]
\[ 2(b + 3) = 3(b - 3) \quad\Longrightarrow\quad 2b + 6 = 3b - 9 \]
\[ b = 15 \text{ kmph} \]
Checking: 18 kmph for 1 hour and 12 kmph for 1½ hours both cover 18 km.
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