Question:A man can row 40 km upstream and 55 km downstream in 13 hours. Also he can row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the man in still water and the speed of the current. 

Answer Let, rate upstream = x km/hr & rate downstream = y km/hr.

Then,` 40/x + 55/y = 13 .......(i)`

and ` 30/x + 44/y = 10 ..... (ii)`

or 40u + 55v = 13 .....(iii)

and 30u + 44v = 10 .... (iv)

where `u = 1/x` and `v = 1/y`

On solving (iii) and (iv) we get `: u = 1/5` and v = 1/11`

:. x = 5 and y = 11

:. Rate in still water` = 1/2 (11 + 5)` kmph = 8 kmph.

Rate of current` = 1/2 (11 - 5)` kmph = 3 kmph 

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