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

Given that:

Total Distance = 32km
Speed in Still Water = 24km/h
Let the speed of the stream be ‘x’ km/h
then, Speed moving upstream = 24-x
Speed moving downstream = 24+x

Now for upstream journey

Time taken = 32/ 24-x hours

For downstream journey

Time taken = 32/ 24+x hours

Difference between timings =1 hr
Time of upstream journey = Time of downstream journey +1 hr

Hence the equation becomes

(32/ 24-x) – (32/ 24+x) = 1

1/32= (1/ 24-x) – (1/ 24+x)

1/32= (24+x-24+x) / 242- x2

242- X2 = 64X

X2 + 64x – 576= 0

On factorising we get

x2 +72x – 8x – 576 = 0

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

(X-8)(x=72)=0

x=8 or x=-72

Speed cannot be negative

Hence X=8

Therefore, the speed of the stream is 8 km/hr

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