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Question
A boat takes 1.6 hours longer to go 36 kms up a river than down the river. If the speed of the water current is 4 km per hr, what is the speed of the boat in still water?
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Solution
Let the speed of the boat in still water be “x”
Time taken to go for up of a river = `36/(x + 4)`
By the given condition
`36/(x - 4) - 36/(x + 4)` = 1.6
`(36(x + 4) - 36(x - 4))/((x + 4)(x - 4)) = 16/10`
`(36[x + 4 - (x - 4)])/(x^2 - 16) = 16/10`
`(36 xx 8)/(x^2 - 16) = 16/10`
16(x2 – 16) = 36 × 8 × 10
x2 – 16 = `(36 xx 8 xx 10)/16`
x2 – 16 = 180
x2 = 180 + 16
x2 = 196
x2 = `sqrt(196)`
= ± 14
The speed of the boat in still water = `(14"km")/"hr"`
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