Discussion
Simran takes twice as long to swim up as to swim down the river and has a speed of 12 km/hr in still water. What is river’s speed?
Answer: D
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
Twice the time means half the speed over the same distance:
\[ \frac{b + r}{b - r} = 2 \quad\Longrightarrow\quad 12 + r = 2(12 - r) \]
\[ 12 + r = 24 - 2r \quad\Longrightarrow\quad 3r = 12 \quad\Longrightarrow\quad r = 4 \text{ km/h} \]
Checking: 16 km/h downstream and 8 km/h upstream. In general, when the upstream time is \( n \) times the downstream time, \( r = b \times \tfrac{n-1}{n+1} \) - here \( 12 \times \tfrac{1}{3} = 4 \).
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