Question

A man can row 30 km downstream and 20 km upstream in 4 hours. he can row 45 km downstream and 40 km upstream in 7 hours. find the speed of man in still water?

Answer 1

HEYA,

HERE IS YOUR ANSWER,

Let's assume speed of the man in still water = x km/h,

And the speed of the stream = y km/h.

As per the question Downstream + upstream

=> 30/(x + y) + 20/(x - y) = 4 ------ (1)

=> 45/(x + y) + 40/(x - y) = 7 ----- (2)

By Solving above equation the speed of man in still water = 12.5 km/h

HOPE IT HELPS YOU,
THANK YOU.

Answer 2

A man can row 30 km downstream and 20 km upstream in 4 hours. he can row 45 km downstream and 40 km upstream in 7 hours.

We have to find the speed of man in still water.

what are downstream and upstream ?

• downstream : when a boat moves along stream, is known as downstream.
• if x is speed of boat in still water and y is speed of stream then, (x + y) is speed of boat in downstream.
• upstream : when a boat moves opposite to stream is known as upstream motion of the boat.
• (x - y) is speed of boat in upstream.

let the speed of man is x km/h and stream is y km/h.

case 1 : the man can row 30 km downstream and 20 km upstream in 4 hrs.

$\frac{30}{(x+y)}+\frac{20}{(x-y)}=4$

let 1/(x + y) = P and 1/(x - y) = Q

⇒30P + 20Q = 4

⇒15P + 10Q = 2 ...(1)

case 2 : he can row 45 km downstream and 40 km upstream in 7 hrs.

$\frac{45}{(x+y)}+\frac{40}{(x-y)}=7$

⇒45P + 40Q = 7 ...(2)

from equations (1) and (2) we get,

⇒4(15P + 10Q) - (45P + 40Q) = 2 × 4 - 7

⇒60P - 45P = 1

⇒P = 1/15 = 1/(x + y)

⇒x + y = 15 km/h ...(3)

and Q = 1/10 = 1/(x - y)

⇒x - y = 10 ...(4)

from equations (3) and (4) we get,

x = 12.5 km/h and y = 2.5 km/h

Therefore the speed of man in still water is 12.5 km/h.