A boat having speed 12 km/h in still water takes 2 hours more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.
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let speed of stream =x
speed of motorboat = 12 km/h
distance= 32km
time taken by motorboat to go downstream= 32/(x+ 12) h
time taken to go upstream = 32/(12-x)
32/(x+12) + 2 = 32/(12- x)
=32/(12- x) - 32/(x+12) = 2
=32(x+12) - 32(12-x) = 2(12-x)(x+12)
=32x + 32*12- 32*12+ 32x = 288 - 2x2
=64x= 288 - 2x2
=32x= 144-x2
= x2 +32x - 144=0
=x2 - 36x + 4x - 144= 0
= (x + 4) • (x - 36)=0
= x -36= 0 or x+4=0
= x=36km/h as x cant be -4 which is negative
so speed of stream is 36km/h
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