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Question
The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
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Solution
Let the speed of stream be x km/hr then
Speed downstream = (8 + x)km/hr.
Therefore, Speed upstream = (8 - x)km/hr
Time taken by the boat to go 15km upstream `15/(8-x)hr`
Time taken by the boat to returns 22km downstream `22/(8+x)hr`
Now it is given that the boat returns to the same point in 5 hr.
So,
`15/(8-x)+22/(8+x)=5`
`(15(8+x)+22(8-x))/((8-x)(8+x))=5`
`(120+15x+176-22x)/(64-x^2)=5`
`(296-7x)/(64-x^2)=5`
5x2 - 7x + 296 - 320 = 0
5x2 - 7x - 24 = 0
5x2 - 15x + 8x - 24 = 0
5x(x-3) + 8(x - 3) = 0
(x - 3)(5x + 8) = 0
x - 3 = 0
x = 3
Or
5x + 8 = 0
5x = -8
x = -8/5
But, the speed of the stream can never be negative.
Hence, the speed of the stream is x = 3 km/hr
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