Question

A motorboat whose speed is 24 km/hr in still water takes one hour more to go 30 km upstream than to return downstream to the same spot. Find the speed of the stream.

Answer 1

Let to be the speed of stream =x



According to the Question;-


Speed of motorboat = 24 km/h


distance of motorboat = 32km

Therefore,


Time taken by motorboat to go downstream= 32/(x+ 24) hr


Time taken by motorboat to go upstream = 32/(24-x)

Again, According to the Question;

   32/(x+24) + 1 = 32/(24- x)


=) 32/(24- x) - 32/(x+24)  = 1


=)32(x+24) - 32(24-x) = (24-x)(x+24)


=) 32x +( 32 x 24 - 32 x 24) + 32x = 242 - x2 


=) 64x= 576 - x2 


= x2 +64x - 576=0


=)x2  +72x - 8x -576 = 0


=) x(x+72) -  8(x-72) =0


=) x -8 = 0
x=8

-'-
x+72=0 (Cant taken)


=) x=8km/h r

Therefore, speed of stream is 8km/h‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎

Answer 2

Hey there !!


[ The question has some error, i.e., u had written 30 km upstream, but the correct form is 32 km upstream. ]


▶ Solution :-

→ Speed of the motorboat in still water = 24 km/hr.

→ Let the speed in the stream be x km/hr .

→ Then, speed upstream = ( 24 - x ) km/hr.

→ Speed downstream = ( 24 + x ) km/hr.

→ Time taken to go 32 km upstream = $\frac{32}{(24 - x)} .$ hrs.

→ Time taken to return 32 km downstream = $\frac{32}{(24 + x)} .$ hrs.

$\therefore \frac{32}{(24 - x)} - \frac{32}{(24 + x)} = 1.$

$= > 32( \frac{1}{(24 - x)} - \frac{1}{(24 + x)} ) = 1.$


$= > \frac{(24 + x) - (24 - x)}{(24 - x)(24 + x)} = \frac{1}{32} .$


$= > \frac{2x}{ {(24)}^{2} - {(x)}^{2} } = \frac{1}{32} .$


$= > \frac{2x}{576 - {x}^{2} } = \frac{1}{32} .$


=> 576 - x² = 64x .

=> x² + 64x - 576 = 0.

=> x² + 72x - 8x - 576 = 0.

=> x( x + 72) -8( x + 72 ) = 0.

=> ( x - 8 )( x + 72 ) = 0.

=> x - 8 = 0 | x + 72 = 0.

=> x = -72 or x = 8.

=> $\huge \boxed{ \boxed{ \bf x = 8 }}$

[ °•° Speed of the stream cannot be negative ].


✔✔ Hence, the speed of the stream is 8 km/hr. ✅✅

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THANKS


#BeBrainly.