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  • A motorboat whose speed is 24 Km/hr in still water takes 1 hour more go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.      

A motorboat whose speed is 24 Km/hr in still water takes 1 hour more go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.

 

 

 

 

 
 
 
 
 

Answers (1)

Total distance = 32 km 

speed of boat in still water = 24 km/hr 

Let the speed of stream be x km/hr 

speed of moving upstream = 24-x 

speed of moving downstream = 24 +x 

time = distance /speed 

\frac{32}{24-x}- \frac{32}{24+x} = 1 \\\\ 32 \left [ \frac{(24+x)- ( 24 - x )}{(24-x)(24+x)} \right ] = 1 \\\\ 32 \left [ \frac{24+x-24+x}{(24 ^2-x^2)} \right ] = 1 \\\\ \frac{32 \times 2x }{24 ^2 - x^2} = 1 \\\\ 64 x = 576 - x^2 \\\\ x^2 + 64 x -576 = 0

x^2 + 72 x- 8x - 576 = 0 \\\\ x ( x +72)- 8 ( x+7 2 ) = 0 \\\\ ( x -8 ) ( x +72 ) = 0 \\\\\ x = 8 \: \: or\: \: x = -72

since speed can not be negative hence x = 8km/hr 

speed of stream = 8 km/hr

Posted by

Ravindra Pindel

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