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  • A motorboat whose speed is 18 km/h in still water takes 1 hr 30 minutes more to go 36 km upstream than to return downstream to the same spot. Find the speed of the stream.    

A motorboat whose speed is 18 km/h in still water takes 1 hr 30 minutes more to go 36 km upstream than to return downstream to the same spot. Find the speed of the stream.

 

 

 

 
 
 
 
 

Answers (1)

Speed of boat in still water =18 \; km

Let the speed of stream be x km/hr.

\text{Speed of boat upstream}=\text{Speed of boat in still water }- \text{Speed of stream.}

\text{Speed of boat upstream}=(18-x) \; km/hr

\frac{\text{Time of upstream journey}}{\text{Speed of boat upstream}} = \frac{\text{distance covered downstream}}{\text{Speed of the boat downstream}}

\frac{36}{(18-x)} = \frac{36}{(18+x)}+1 \frac{1}{2}

\frac{36}{(18-x)} - \frac{36}{(18+x)} = \frac{3}{2}

\frac{648+36x-648+36x}{(18-x)(18+x)} = \frac{3}{2}

72x =(324-x^2) \left ( \frac{3}{2} \right )

144x =972-3x^2

3x^2+144x-972=0

Divide by 3

x^2+48x-324=0x=6,x\neq -54Th

x^2-6x+54x-324=0

x(x-6)+54(x-6)=0

(x-6)(x+54)=0

The speed of the stream 1 is 6 km/hr.

Posted by

Ravindra Pindel

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