SOLUTION: 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

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Question 230679: 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 accidently openedwhen the tank is full, then how long will it take to empty the tank?
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
It doesn't really matter how big the tank is,
because the 2 pipes will just get bigger and
bigger to fill or empty a bigger tank.
I'll say the tank holds 90 gallons when it's full
The rate of filling an empty tank is:
gallons/min
The rate of emptying a full tank is:
gallons/min
(the minus sign is the only way I can
tell if I'm emptying of filling)
----------------------------------------
If both outlet and inlet are opened, I simply
add the 2 rates, still using the minus for emptying
gallons/min

gallons/min
The tank is emptying at this rate with both pipes open
min
With both pipes open, the 90 gallon tank
empties in 90 min

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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?
:
Here's another way to do it
;
Let t = time to empty with both valves opened
:
Let an empty tank = 1
therefore:
+ for emptying; - for filling
:
- = 1
Multiply by 90, results:
3t - 2t = 90
t = 90 min to drain the tank with both valves open