# A motor boat whose speed in still water is 18km/hr takes i hour more to go 24km upsteamthan to return downstream to the same spot.find the speed of stream

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by nandunadz

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by nandunadz

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speed of the current be x,

T(up stream) - T(down stream) = 1 hour

24/(18-x) - 24/(18+x) = 1hr

24(18+x - 18 + x)/(18^2 - x^2) = 1

which will give you

x = -54 which is absurd

and

x = 6 kmph

so

Speed of the stream = 6 kmph -

Speed of boat = 18 km/h

Speed while upstream = (18 - x) km/h

Speed while downstream = (18 +x) km/h

Distance = 24km

Time taken to travel upstream = distance/speed = 24/(18 - x) hrs

Time taken to travel downstream = distance/speed = 24/(18 + x) hrs

According to the question

24/(18-x) +1 = 24/(18+x)

⇒(24+18 - x) /(18 - x) = 24/(18+x)

⇒(42 -x )/(18-x) = 24/(18+x)

⇒(42-x)(18+x) = 24(18-x)

⇒(42)(18) + 42x -18x -x² = (24)(18) - 24x

⇒756 + 24x -x² = 432 - 24x

⇒756 - 432 +24x + 24x -x² = 0

⇒324 +48x -x² = 0

⇒0 = x² - 48x -324

⇒x² - 48x -324 = 0

⇒ x² - 2(x)(24) +24² - 24² - 324 = 0

⇒ (x -24)² -576 -324 =0

⇒ (x -24)² -900 = 0

⇒ (x-24)² = 900

⇒ (x-24) = + or - √900

⇒ (x-24) = +30 or -30

⇒ x -24 = 30 or x-24 = - 30

⇒ x = 54 or x =-6

speed of stream = 54km

i am not sure of this