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?

Click here to see ALL problems on Rate-of-work-word-problems

Question 98661: 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?
Time taken by horse A to fill the pool = 6 hrs
Time taken by horse B to fill the pool = y hrs
Time taken by both together to fill the pool = x hrs
therefore y = x+3........(1)
qn'ty filled by horse A in 1 hr = 1/6
qn'ty filled by horse B in 1 hr = 1/y
qn'ty filled by both in 1 hr = 1/x
therefore 1/x = 1/6+1/y........(2)
substituting for y in eq'n (2) we get
1/x = 1/6+1/(x+3)
1/x = x+3+6/6(x+3)
1/x = x+9/6(x+3)
6(x+3) = x(x+9)
6x+18 = x^2+9x
x^2+9x-6x-18 = 0
x^2+3x-18 = 0
x^2+6x-3x-18 = 0
x(x+6)-3(x+6)= 0
(x+6)(x-3)= 0
substituting for x in eq'n (1) we get y = x+3
x-3 = 0 or x = 3 therefore y = 3+3 = 6
Horse B would take 6 hrs to fil the pool