Question

A motorboat whose speed in still water is $18$ km/h, takes $1$ hour more to go $24$ km 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 $=18$ km/hr

Speed of the boat in upstream $=(18-x)$ km/hr

Speed of the boat in downstream $=(18+x)$ km/hr

Distance between the places is $24$ km.

Time to travel in upstream $\frac{d}{18–x}$ hr

Time to travel in downstream $\frac{d}{18+x}$ hr

Difference between timings $=1$ hr

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

Therefore, $\frac{24}{18–x}=\frac{24}{18+x}+1$

$\Rightarrow \frac{24}{18–x}-\frac{24}{18+x}=1$

$\Rightarrow \frac{432+24x-432+24x}{(18-x)(18+x)}=1$

$\Rightarrow 48x=324–x^2$

$\Rightarrow x^2+48x-324=0$

$\Rightarrow x^2+54x-6x-324=0$

$\Rightarrow x(x+54)-6(x+54)=0$

$\Rightarrow (x+54)(x-6)=0$

So, $x=-54$ or $6$ (speed of the stream cannot be negative)

Therefore, speed of stream is $6$ km/hr.