A motor boat can travel at 9 km/hr in still water. It travelled 65 km downstream in river and then returned back taking altogether 18 hours. The speed of the stream is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4 km/hr
$\text{Speed in still water} = 9 \text{ km/hr},\;\; \text{stream} = v$
$\text{Downstream speed} = 9+v,\;\; \text{Upstream speed} = 9-v$
$\frac{65}{9+v} + \frac{65}{9-v} = 18$
$65\left(\frac{1}{9+v} + \frac{1}{9-v}\right)=18$
$65\left(\frac{18}{81 - v^2}\right)=18$
$\frac{1170}{81 - v^2}=18$
$1170 = 18(81 - v^2)$
$1170 = 1458 - 18v^2$
$18v^2 = 288$
$v^2 = 16 \Rightarrow v=4$
The speed of the stream is $4$ km/hr.