Discussion
3 towns P, Q and R are located at the bank of a stream. Distance of Q from P and R is same. Jeet rows from P to Q and Q to P in total 10 hours. Jeet also requires 4 hours to row from P to R. If the stream flows at a consistent rate what will be the ratio of Jeet’s speed in still water and speed of stream?
Answer: B
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
Let the distance \( PQ = QR = d \), with Q and R downstream of P.
P to R is \( 2d \) downstream in 4 hours:
\[ \frac{2d}{b + r} = 4 \quad\Longrightarrow\quad \frac{d}{b + r} = 2 \]
The round trip P–Q–P takes 10 hours:
\[ \frac{d}{b + r} + \frac{d}{b - r} = 10 \quad\Longrightarrow\quad 2 + \frac{d}{b - r} = 10 \]
\[ \frac{d}{b - r} = 8 \]
Dividing the two results eliminates \( d \):
\[ \frac{b + r}{b - r} = \frac{8}{2} = 4 \quad\Longrightarrow\quad b + r = 4b - 4r \]
\[ 5r = 3b \quad\Longrightarrow\quad \frac{b}{r} = \frac{5}{3} \]
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