SOLUTION: A water tank can be filled by an inlet pipe in 9 hours. It takes 4 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are ope

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A water tank can be filled by an inlet pipe in 9 hours. It takes 4 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are ope      Log On


   

Question 890791: A water tank can be filled by an inlet pipe in 9 hours. It takes 4 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = time it takes to fill the tank if both pipes are open
Then the tank fills at the rate of 1/x tank per hour when both pipes are open
The water tank is filled at the rate of 1/9 tank per hour
The water tank is emptied at the rate of 1/(9*4)=1/36 tank per hour
So our equation to solve is:
1/9-1/36=1/x
4/36-1/36=1/x
3/36=1/x
3x=36
x=12 hrs---time it takes to fill the tank with both pipes open
CK
In 12 hours the inlet pipe fills (1/9)*12 =4/3 tank
But in 12 hrs the drain pipe drains(1/36)*12=1/3 tank
4/3 - 1/3 =3/3=1 tank
Hope this helps---ptaylor