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Question
A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.
Solution
Let the speed of the stream be v km/h
Given that, speed of a person rowing in still water = 5 km/h
The speed of a person rowing in downstream = (5 + v) km/h
And the speed of a person has rowing in upstream = (5 – v) km/h
Now, the person takes time to cover 40 km downstream,
t1 = `40/(5 + v)` hours ...`[because "speed" = "distance"/"time"]`
Now, the person takes time to cover 40 km upstream,
t2 = `40/(5 - v)` hours
By condition,
t2 = t1 × 3
⇒ `40/(5 - v) = 40/(5 + v) xx 3`
⇒ `1/(5 - v) = 3/(5 + v)`
⇒ 5 + v = 15 – 3v
⇒ 4v = 10
∴ v = `10/4` = 2.5 km/h
Hence, the speed of the stream is 2.5 km/h.
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