Question

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

Answer 1

Let the speed of the steamer in still water is $xkm/h$ and distance is $d$.

Then, speed of steamer downstream $\left(u\right)=$ speed of steamer in still water+speed of stream$=x+1$

Speed of steamer upstream $\left(v\right)=$speed of steamer in still water-speed of stream$=x-1$

Distance covered by steamer upstream $\left(d\right)=10(x-1)$ ......(1)

Distance covered by steamer downstream $\left(d\right)=9(x+1)$ ......(2)

From equation (1) and (2),

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

$10x-10=9x+9$

$10x-9x=9+10$

$x=19km/h$

Substituting this value in equation(1),

$Distance\left(d\right)=10(19-1)=180km$

Hence, the speed of the steamer in still water is $19km/h$ and the distance between the ports is $180km$.