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A boat which travels at the rate of 10.5...

A boat which travels at the rate of 10.5 km/hr downstream takes 3 times as long time to go to a certain distance up a river as to go the same distance down. Find the rate at which stream flows.

Text Solution

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Let the speed of stream = x km/hr
and the speed of boat in still water = y km/hr
`therefore` Speed of boat downstream = (x + y) km/hr
and speed of boat upstream = (y - x) km/hr
Let the distance be D km.
`therefore` According to the problem,
x + y = 10.5 ...(1)
Also, time taken by boat upstream = 3 `xx` time taken by boat downsteam
implies `(D)/(y - x) = 3 xx (D)/(10.5)`
`implies y - x = 3.5`
Adding equations (1) and (2), we get
2y = 14 implies y = 7
Putting y = 7 in equation (1), we get
x + 7 = 10.5 implies x = 3.5
Hence, speed of stream = 3.5 km/hr
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