SOLUTION: Filling a tank. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes wit

Question 206797This question is from textbook Elementary and Intermediate Algebra
: Filling a tank. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank? This question is from textbook Elementary and Intermediate Algebra

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes to empty the tank when both pipes are left open
Then, with both pipes open ,the tank empties at the rate of 1/x tank per min
Drain pipe empties at the rate of 1/30 tank per min
Inlet pipe fills at the rate of 1/45 tank per min
Then, with both pipes open ,the tank empties at the rate of 1/30-1/45 tank per min
So, our equation to solve is
1/30-1/45=1/x multiply each term by 90x
3x-2x=90
x=90 min------------------amount of time to empty tank when both pipes are left open
CK
In 90 min, inlet pipes pours in 90(1/45) or 2 tanks of water
In 90 min, drain pipe drains 90(1/30) or 3 tanks of water
So the two tanks of water poured in by the inlet pipe in 90 min plus the full tank that was already there equals the 3 tanks that were emptied by the drain pipe.
Hope this helps---ptaylor
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