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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.
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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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