Question

A motor-boat takes $2$ hours more to cover a distance of $30km$ upstream than it takes to cover the same distance downstream.If the speed of the stream is $2km/hr$. Find the speed of boat is still water.

Answer 1

Let speed in still water be $x$

Speed of boat during upstream journey $=x-2$

Speed of boat during downstream journey$=x+2$

Time taken for upstream journey $=\frac{30}{x-2}$

Time taken for downstream journey$=\frac{30}{x+2}$

According to the given condition,

$\frac{30}{x-2}=\frac{30}{x+2}+2$

$\frac{30}{x-2}-\frac{30}{x+2}=2$

$\frac{30(x+2-x+2)}{x^2-4}=2$

$60=x^2-4$

$x^2=64$

$x=8$