Question

Pratik takes $8$ hours to travel $36$ km downstream and return to the same spot the speed of boat in still water is $12$ kilometre per hour find the speed of water current

Answer 1

Let the speed of the current be $x$ km/hr.

Pratik goes $36$ km downstream.

$\therefore$ Distance covered by the Pratik in Downstream $=36$ km.

Speed of the Pratik in downstream $=(12+x)$ km/hr.

$\therefore$ Time taken $=\frac{36}{(12+x)}$

Now, He also returned to the same spot.

$\therefore$ Distance covered in upstream $=36$ km.

Speed of the Pratik in upstream $=(12-x)$ km/hr.

$\therefore$ Time taken $=\frac{36}{(12-x)}$

Now,

Time taken in upstream $+$ Time taken in downstream $=8$ hrs.

$\therefore \frac{36}{(12-x)}+\frac{36}{(12+x)}=8$

$\Rightarrow 36(12+x)+36(12-x)=8(12+x)(12-x)$

$\Rightarrow 36(12+x+12-x)=8(144-12x+12x-x^2)$

$\Rightarrow 36\times 24=8(144-x^2)$

$\Rightarrow 36\times 3=144-x^2$

$\therefore x^2=144-108$

$\therefore x=\sqrt{36}$

$\Rightarrow x=+6$ or $-6$

$-6$ cannot be possible.

$\therefore$ Speed of the current is $6$ km/hr.