SOLUTION: A pipe can fill a tank in 3 hours. Another pipe can empty the tank in 6 hours. If the tank is empty and both pipes are open, how many hours will it take to fill the tank?

Question 956567: A pipe can fill a tank in 3 hours. Another pipe can empty the tank in 6 hours. If the tank is empty and both pipes are open, how many hours will it take to fill the tank?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The rate of filling of the 1st pipe is:
[ 1 tank filled ] / [ 3 hrs ]
-------------------------------
The rate of emptying of the 2nd pipe is:
-[ 1 tank emptied ] / [ 6 hrs ]
---------------------------
Notice that the emptying rate has to have
a minus sign to make it opposite the
filling rate
-----------------
Let = the rate of filling with
both pipes open
Add the rates to get the rate working together

Multiply both sides by

It will take 6 hrs to fill the tank
----------------------------
This makes sense because in 6 hrs, the 1st pipe
fills the tank twice
In that same 6 hrs, the 2nd pipe empties the
tank once
and you are left with 1 tank full

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