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Question 206806This question is from textbook Elementary and intermediate algebra
: ``Filing a tank. A water tank has an inlet pipe and a drain pipe. A full tank came 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 accidently opened when the tank is full, then how long will it take to empty the tank? Ok, drain pipe=30 minutes while the inlet pipe=45 minutes. So would it take 30d/45i=2/3. I am lost. Could you explain to me step by step so I can understand. I did receive an earlier answer of 90 minutes but I need a second opinion. If it takes 30 minutes for the tank to empty and 45 minutes to fill. wouldn't the tank continue to fill because the inlet is open? Please explain to me !!
This question is from textbook Elementary and intermediate algebra
Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Previous solution by ptaylor:
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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The water drains faster than the inlet fills - 30 mins to drain, 45 mins to fill, so the net is that the level decreases.
The inlet fills the tank in 45 minutes, so it adds 1/45 of a tank per minute.
The drain empties the tank in 30 minutes, so it loses 1/30 of the tank per minute.
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Each minute, 1/45 is added and 1/30 is drained.
The amount drained is 1/30, but 1/45 is added. The difference the net, is
1/30 - 1/45 = 1/90.
1/90 of the tank is drained per minute.
--> 90 minutes to empty the tank.
Answer by ankor@dixie-net.com(22740)  (Show Source):
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