Discussion
Michel can swim in still water at the rate of 6km per hour. After swimming in a stream, she realized that she takes twice the time to go upstream as she takes to go downstream. What is speed of the current?
Answer: B
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
Time is inversely proportional to speed over the same distance, so taking twice as long upstream means going half as fast:
\[ \frac{b + r}{b - r} = 2 \]
\[ 6 + r = 2(6 - r) = 12 - 2r \]
\[ 3r = 6 \quad\Longrightarrow\quad r = 2 \text{ km/h} \]
Checking: downstream 8 km/h and upstream 4 km/h - exactly double.
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