Discussion
A boat takes 90 minutes less to travel 36 km downstream than to travel the same distance upstream. If the speed of the stream is 2 km/hr, what is the speed of the boat in still water ?
Answer: C
Correct answer: 10 km/hr
With \(b\) the still-water speed, the two times differ by \(1\tfrac{1}{2}\) hours:
\[\frac{36}{b-2} - \frac{36}{b+2} = 1.5\]
\[36 \cdot \frac{(b+2)-(b-2)}{b^2 - 4} = 1.5 \quad\Longrightarrow\quad \frac{144}{b^2 - 4} = 1.5\]
\[b^2 - 4 = 96 \quad\Longrightarrow\quad b^2 = 100 \quad\Longrightarrow\quad b = 10 \text{ km/hr}\]
Checking: 36 km takes 3 hours downstream at 12 km/hr and 4.5 hours upstream at 8 km/hr.
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