SOLUTION: Two pipes are used to fill a water tank. The first pipe can fill the tank in 4 hours. The two pipes together can fill the tank in 2 hrs less time than the second pipe alone. How lo

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Two pipes are used to fill a water tank. The first pipe can fill the tank in 4 hours. The two pipes together can fill the tank in 2 hrs less time than the second pipe alone. How lo      Log On


   

Question 909185: Two pipes are used to fill a water tank. The first pipe can fill the tank in 4 hours. The two pipes together can fill the tank in 2 hrs less time than the second pipe alone. How long will it take for the second pipe to fill the tank?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Two pipes are used to fill a water tank. The first pipe can fill the tank in 4 hours. The two pipes together can fill the tank in 2 hrs less time than the second pipe alone. How long will it take for the second pipe to fill the tank?

let filling the tank be considered as 1 job
The first pipe can fill the tank in 4 hours.
so it does 1/4 of the job in 1 hour
let second pipe take x hours
it does 1/x of the job in 1 hour
both pipes take x-2 hours
they do 1/(x-2) of the job in 1 hour
1/4 + 1/x = 1/(x-2)
1/(x-2)-1/x =1/4
(x-x+2)/(x(x-2)) =1/4
2/(x(x-2))=1/4
x(x-2)=8
x^2-2x=8
x^2-2x-8=0
x^2+4x-2x-8=0
x(x+4)-2(x+4)=0
(x-2)(x+4)=0
x=2 OR -4
ignore negative
x=2
second pipe takes 2 hour