SOLUTION: A hose can fill a swimming pool in 6 hours. Another hose needs 3 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool?

Question 98649: A hose can fill a swimming pool in 6 hours. Another hose needs 3 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool?
Answer by malakumar_kos@yahoo.com(315) (Show Source): You can put this solution on YOUR website!

A hose can fill a swimming pool in 6 hours. Another hose needs 3 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool?
let the two horses be A & B
time taken by horse A = 6 hrs
time taken by horse B = y hrs
time taken by A & B together = 6+x hrs
y = 6+x+3
y = x+9...........(1)
Qu'ty of pool filled by A in 1 hr = 1/6
Qu'ty of pool filled by B in 1 hr = 1/y
Qu'ty of pool filled by A & B in 1 hr = 1/(6+x)
1/(6+x) = 1/6+1/y
1/(6+x) = y+6/6y
6y = (6+y)(6+x)
6y = 36+6x+6y+xy
-6x-xy = 36.......(2)
substituting for y in (2) we get -6x - x(x+9)= 36
-6x -x^2-9x = 36
-x^2-15x-36 = 0
x^2+15x+36 =0
Factors of 36 are 12 &3 x^2+12x+3x+36 = 0
x(x+12)+3(x+12)= 0
(x+12)(x+3) = 0
x+12 = 0 or x = -12
x+3 = 0 or x = -3
time taken by horse B to fill the pool = y = x+9
if x = -3 then y = -3+9 = 6 hrs
if x = -12 then y = -12+9 = -3
-3 hrs cannot be considered so x= 6 hrs is the required value

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