Question

A steamer goes downstream and covers the distance between two parts in $5$ hours, while it covers the same distance upstream in $7$ hours. If the speed of the stream is $3$ km/h, then the speed of the streamer in still water is

Answer 1

Let the speed of the streamer in still water $=x$ km/hr

the speed of the stream is $3$ km/hr

Let the distance covered $=d$ km

Speed downstream $=x+3$ km/hr

Time taken $=5$ hr

Distance$=$speed $\times$ time

$d=5(x+3)$

$d=5x+15$ ............ (1)

Speed upstream $=x-3$ km/hr

Time taken $=7$ hr

Distance$=$speed $\times$ time

$d=7(x-3)$

$d=7x-21$ ........... (2)

From (1) and (2),

$7x-21=5x+15$

$7x-5x=15+21$

$2x=36$

$x=18$ km/hr