Question

A motor boat, whose speed is $20km/hr$ in still water takes $1$ hour more to go $48km$ upstream than to return downstream to the same spot. Find the speed of the stream.

Answer 1

Let, the speed of the stream be $x$ km/hr

Speed of boat in still water $=20$ km/hr

$\therefore$Speed of boat with downstream $20+x$ km/hr

$\therefore$ Speed of boat with upstream $20-x$ km/hr

As per given condition

$\frac{48}{20-x}-\frac{48}{20+x}=1$

$⟹48[\frac{1}{20-x}-\frac{1}{20+x}]=1$

$⟹\left[\frac{20+x-20+x}{(20-x)(20+x)}\right]=\frac{1}{48}$

$⟹\frac{2x}{400-x^2}=\frac{1}{48}$

$⟹96x=400-x^2$

$⟹x^2+96x-400=0$

$⟹x^2+100x-4x-400$

$⟹x(x+100)-4(x+100)=0$

$⟹(x-4)(x+100)=0$

Either, $x=4$ or $x=-100$

$\because$ Speed cannot be negative $\therefore x=4$ km/hr is considered.

$\therefore$ the speed of the stream $=4$ km/hr