Question

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

Answer 1

Total Distance = 32km
Speed in Still Water = 24km/hr
Let the speed of stream be 'x' kmph
then, Speed moving upstream = 24-x
         Speed moving downstream = 24+x
We know that $\frac{Distance}{Speed} \frac$ is time 
$</span>{32}{24-x} - \frac{32}{24+x} = 1$
On reducing it to a quadratic equation,
we get - $x^{2} + 64x-576=0$
On solving it by splitting the middle term method (8&72 as factors) we get,
x = 8 or -72
Since, the speed cannot be negative, x = 8
Therefore, the speed of the stream is 8 km/hr

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the speed of stream be x km/h.

Speed of upstream = (24 - x) km/h.

Speed of downstream = (32 - x) km/h.

Time taken to go 32 km upstream = 32/(24 - x) hr

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

According to the Question,

⇒ 32/(24 - x) - 32/(24 + x) = 1

⇒ 1/(24 - x) - 1/(24 + x) = 1/32

⇒ (24 + x) - (24 - x)/(24 - x) (24 + x) = 1/32

⇒ 2x/(576 - x²) = 1/32

⇒ 576 - x² = 64x

⇒ x² + 64x - 576 = 0

⇒ x² + 72x - 8x - 576 = 0

⇒ x(x + 72) - 8(x + 72) = 0

⇒ (x + 72) (x - 8) = 0

⇒ x + 72 = 0 or x - 8 = 0

⇒ x = - 72, 8 (As x can' be negative)

⇒ x = 8

Hence, the speed of the stream is 8 km/h.

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