Question

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

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Answer 1

Let the speed of the stream be x km/hr

Speed of the boat in still water =24 km/hr

Speed of the boat in upstream =(24−x) km/hr

Speed of the boat in downstream =(24+x) km/hr

Distance between the places is 32 km.

Time to travel in upstream =24–xd hr

Time to travel in downstream =24+xd hr

Difference between timings =1 hr

Time of upstream journey = Time of downstream journey +1 hr

Therefore, 24–x32=24+x32+1

24–x32−24+x32=1

(24−x)(24+x)768+32x−768+32x=1

64x=576–x2

x2+64x−576=0

On factoring, we get

(x+72)(x−8)=0

So, x=−72 or 8 (speed of the stream cannot be negative)