Discussion

Raj swims 26 km downstream in same time as 14 km upstream. What is his speed in still water if speed of stream is 3 km/hr?

Answer: A

Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then

\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]

Equal times mean the two distances are in the same ratio as the two speeds.

\[ \frac{26}{b + 3} = \frac{14}{b - 3} \]

\[ 26(b - 3) = 14(b + 3) \quad\Longrightarrow\quad 26b - 78 = 14b + 42 \]

\[ 12b = 120 \quad\Longrightarrow\quad b = 10 \text{ km/h} \]

Checking: 26 km at 13 km/h and 14 km at 7 km/h both take exactly 2 hours.

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