Discussion

The speed of boat in still water is 20 km/hr. If it travels 26 km downstream and 14 km upstream in same time, what is the speed of the stream?

Answer: C

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 distances are in proportion to the speeds:

\[ \frac{26}{20 + r} = \frac{14}{20 - r} \]

\[ 26(20 - r) = 14(20 + r) \quad\Longrightarrow\quad 520 - 26r = 280 + 14r \]

\[ 240 = 40r \quad\Longrightarrow\quad r = 6 \text{ km/h} \]

Checking: 26 km at 26 km/h and 14 km at 14 km/h both take exactly one hour.

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