A man can row a boat in still water at the rate of 17 km/hr. He finds that it takes him thrice as long to row upstream of a river as to row downstream of the same river. The speed of the stream is,
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 8.5 km/hr
Let the speed of the stream be v km/hr.
\( \text{Upstream speed}=17-v \)
\( \text{Downstream speed}=17+v \)
For the same distance, time is inversely proportional to speed. Upstream takes three times as long, so the downstream speed is three times the upstream speed:
\( 17+v=3(17-v) \)
\( 17+v=51-3v \)
\( 4v=34 \)
\( v=8.5\ \text{km/hr} \)
Shortcut: If upstream time : downstream time = 3 : 1, then boat speed : stream speed = (3 + 1) : (3 − 1) = 2 : 1, so the stream speed is \( \frac{17}{2}=8.5 \) km/hr.
CBSE Applied Mathematics (Class XII):
Boats and Streams
