Question

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

Answer 1

Let
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 - 

Answer 2

Let the speed of the stream be x km/h
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