Question

A steamer goes downstream from one point to another in $9$ hours. It covers the same distance upstream in $10$ hours. If the speed of the stream be $1$ km/hr, find the speed of the steamer in still water and the distance between the ports.

Answer 1

It is given that the speed of the stream is $1$ km/h.

Let the speed of the steamer in still water be $x$ km/h.

$\therefore$Downstream speed = $(x+1)$ km/h

Upstream speed = $(x-1)$ km/h

The downstream and upstream distances are same; therefore, we have:

$\Rightarrow 9(x+1)=10(x-1)$

$\Rightarrow 9x+9=10x-10$

$\Rightarrow x=19$

$\therefore$Speed of the steamer in still water = $19$ km/h.

Distance between the ports = $9(19+1)=180$ km.