A motor boat whose speed is $24\ km/hr$ in still water takes one hour more to go to $32\ km$ upstream than to return downstream to the same spot. Find the speed of the stream.

Given: A motor boat whose speed is $24\ km/hr$ in still water takes one hour more to go to $32\ km$ upstream than to return downstream to the same spot.

To do: To find the speed of the stream.

Solution: 


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

$\Rightarrow \frac{32}{24–x}-\frac{32}{24+x}=1$
​
$\Rightarrow ​\frac{768+32x−768+32x}{(24−x)(24+x)}=1$
​
$\Rightarrow 64x=576–x^{2}$
 
$\Rightarrow x^{2}+64x−576=0$

On factoring, we get

$\Rightarrow (x+72)(x−8)=0$

$\Rightarrow x=−72$ or $8$ 

$\because$ Speed can't be negative

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

Updated on: 10-Oct-2022

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