Question

A person can row 50 kms upstream and 70 kms downstream in 4 hours. He can row 35 kms downstream and 75kms upstream in 4 hours. Find the speed of the person in still water and the speed of the current.

Answer 1

let the speed in still water be x

and speed of current = y

50/(x-y) + 70/(x+y) = 4 -----------(1)

75/(x-y) + 35/(x+y) = 4 -----------(2)

let 1/(x-y) = u and 1/(x+y) = v

so, 50u + 70v = 4 ----------(3)

75u + 35v = 4 ------------(4)

subtracting (3) from (4) we get,

25u - 35v = 0

25u = 35v

5u = 7v

u = 7v/5 ------(5)

putting in (3)

50(7v/5) + 70v = 4

70v + 70v = 4

140 v = 4

v = 4/140

v = 1/35

putting value of v in (5)

u = 7v/5

u = 7/(5*35)

u = 1/25

so we have u = 1/25 and v = 1/35

1/(x-y) = u and 1/(x+y) = v

1/(x-y) = u , putting value of u here we get 1/(x-y) = 1/25

x-y = 25 ----------(6)

similarly putting value of v we get

1/(x+y) = v , 1/(x+y) = 1/35,

x+y = 35 -----------(7)

solving 6 and 7 we get

x-y = 25 and x+y = 35

x = 25+y putting in (7) we get

25+y+y = 35

2y = 10

y = 5

and x = 30

so speed in still water is 30kmph and speed of current is 5kmph