Question

A motor boat whose speed is 18 Km/h in still water 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

Given:-

Speed of boat $=18km/hr$

Distance $=24km$

Let $x$ be the speed of stream.

Let $t_1$ and $t_2$ be the time for upstream and downstream.

As we know that,

$\text{speed}=\frac{\text{distance}}{\text{time}}$

$\Rightarrow \text{time}=\frac{\text{distance}}{\text{speed}}$

For upstream,

Speed $=(18-x)km/hr$

Distance $=24km$

Time $=t_1$

Therefore,

$t_1=\frac{24}{18-x}$

For downstream,

Speed $=(18+x)km/hr$

Distance $=24km$

Time $=t_2$

Therefore,

$t_2=\frac{24}{18+x}$

Now according to the question-

$t_1=t_2+1$

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

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

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

$\Rightarrow 48x=(18-x)(18+x)$

$\Rightarrow 48x=324+18x-18x-x^2$

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

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

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

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

$\Rightarrow x=-54\text{or}x=6$

Since speed cannot be negative.

$\Rightarrow x\ne -54$

$\therefore x=6$

Thus the speed of stream is $6km/hr$

Hence the correct answer is $6km/hr$.