Question
At his usual rowing rate , Rahul can travel 12 miles downstream in a certain river in 6 hours less than it take him o travel the same distance upstream. But if he could double his usual rowing rate for his 24 mile round trip , the downstream 12 miles would then take only one hour less han he upstream 12 miles. what is he speed of the current in miles per hour ?
Answer: Option D
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Let the speed in still water be `x` mph and the speed of the current be y mph . Then speed upstream =`(x - y)`;
Speed downstream = `(x + y)`
`:.` `12/(x - y) - 12 /(x + y) = 6 hArr 6(x^2 - y^2 ) = 24 y hArr x^2 - y^2 = 4y`
`hArr x^2 = (4y + y^2).`..................................................(i)
And `12/(2x -y) - 12/(2x + y) = 1 hArr 4x^2 - y^2 = 24y hArr x^2 = (24y + y^2)/(4)` ...................................(ii)
From (i) and (ii) , we have :
`4y + y^2 = (24y + y^2)/(4) hArr 16y + 4y^2 = 24 y + y^2 hArr 3 y^2 = 8y hArr y = 8/3`
`:.` Speed of the current = `8/3` mph = `2 2/3`mph.
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