A motor boat whose speed in still water is 18 km/hr, takes 1 hour more to go 24 km upstream than o return to the same spot.

Question:

A motor boat whose speed in still water is 18 km/hr, takes 1 hour more to go 24 km upstream than o return to the same spot. Find the speed of the stream.

Solution:

Let the speed of the stream be $x \mathrm{~km} / \mathrm{hr}$.

Given :

Speed of the boat $=18 \mathrm{~km} / \mathrm{hr}$

$\therefore$ Speed downstream $=(18+x) \mathrm{km} / \mathrm{hr}$

Speed upstream $=(18-x) \mathrm{km} / \mathrm{hr}$

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

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

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

$\Rightarrow \frac{2 x}{18^{2}-x^{2}}=\frac{1}{24}$

$\Rightarrow 324-x^{2}=48 x$

$\Rightarrow 324-x^{2}-48 x=0$

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

$\Rightarrow x^{2}+(54-6) x-324=0$

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

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

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

$\Rightarrow x=-54$ or $x=6$

The value of $x$ cannot be negative; thereore, the speed of the stream is $6 \mathrm{~km} / \mathrm{hr}$.

 

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