Question

A steamer goes in downstream from one port to another in 4hours. It covers the same distance in upstream in 5 hours. If the speed of the stream be 2 km/h, find the distance between the two ports.

Answer 1

Let the distance between the two ports = x km.
Given, the speed of the stream is 2 km/h
Let the speed of man in still water = y km/h.
Relative speed upstream = (y - 2) km/h
Relative speed downstream = (y + 2) km/h

Then, time taken to go upstream = `x/(y - 2)"hrs"`

Then, time taken to go downstream = `x/(y + 2)"hrs"`

Also, given steamer goes in downstream from one port to another in 4hours.

⇒ `x/(y + 2)` = 4

⇒ x = 4y + 8 --(1)
Also, It covers the same distance in upstream in 5 hours

⇒ `x/(y - 2)` = 5

⇒ x = 5y - 10 ---(2)
Solving, (1) and (2), we get:
4y + 8 = 5y - 10
⇒ y = 18 km/hr.
x = (4x 18 + 8) km
= (72 + 8) km
= 80 km.