Question

A motor boat whose speed is $24km/h$ in still water takes $1hour$ more to go $32km$ 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 the boat in still water $=24$ km/hr

Speed of the boat in upstream $=(24-x)$ km/hr

Speed of the boat in downstream $=(24+x)$ km/hr

Distance between the places is $32$ km.

Time to travel in upstream $=\frac{d}{24–x}$ hr

Time to travel in downstream $=\frac{d}{24+x}$ hr

Difference between timings $=1$ hr

Time of upstream journey $=$ Time of downstream journey $+1$ hr

Therefore, $\frac{32}{24–x}=\frac{32}{24+x}+1$

$\frac{32}{24–x}-\frac{32}{24+x}=1$

$\frac{768+32x-768+32x}{(24-x)(24+x)}=1$

$64x=576–x^2$

$x^2+64x-576=0$

On factoring, we get

$(x+72)(x-8)=0$

So, $x=-72$ or $8$ (speed of the stream cannot be negative)

Therefore, speed of stream is $8$ km/hr.