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Question 253212: 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 empty tank can be filled in 45 minutess with the inlet pipe opened. If both pipes are accidently opened when the tank is full, then how long would it take to empty the tank?
I believe this is a trick question and can possible be unknown.
Found 4 solutions by drk, Greenfinch, richwmiller, Earlsdon:
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! This is a job / time question. Here are the things we need:
J1 = job of inlet pipe
J2 = job of drain pipe
T1 = time of inlet pipe
T1 = time of drain pipe
x = time together
Tj = total number of tanks.
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The basic formula is
(i) (J1/T1)*(x) + (J2/T1)*(x) = Tj
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From this we can fill in some information:
-(1/30)*(x) + (1/45)*(x) = 1.
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Solving, we get:
-3x + 2x = 90, which means x = -90
Since x will be negative, there is no solution based on the information given. If the 30 and 45 were reversed, then we would get an answer.
Answer by Greenfinch(383)  (Show Source):
You can put this solution on YOUR website! Tank is full = 1
Tank is empty = 0
Rate of filling is t/30
Rate of emptying is t/45
The condition is therefore 1-(t/30) + (t/45) = 0
LCM is 90 so 90/90 -(3t - 2t)/90 = 0
or 90 -(3t - 2t)=0
90 -t = 0
t = 90 (minutes)
The problem gets more difficult if the rate of emptying depends on the level of water left in the tank, but this is not the case here.
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! We had a similar problem in the last week or so.
This version starts with a full tank and drains faster than it fills.
t/30-t/45=1
Let's think about this.
If the fill pipe were closed it would take 30 minutes
So after 30 minutes the original water is gone.
In the meantime, it has filled up for 30 minutes. Let's deal with a complete refill.
It can fill in 45 minutes but has only has 30 minutes so it refilled 2/3
So after 45 minutes it will have filled again but the first fill is gone and the drain has had 15 minutes to empty it.
So it emptied half of it. To empty all of it it needs another 45 minutes.
So it would take 90 minutes to empty the full tank with the fill pipe opened.
Answer by Earlsdon(6294) (Show Source):
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