SOLUTION: At 1 pm, Poseidon opened pipe A to fill an empty tank with water. Two hours later, Zeus opened pipe B which also fills the tank, but accidentally opened pipe X which drains the tan

Question 768558: At 1 pm, Poseidon opened pipe A to fill an empty tank with water. Two hours later, Zeus opened pipe B which also fills the tank, but accidentally opened pipe X which drains the tank. At 4 pm, evil Hades closed both pipes A and B. With pipe X left open, the tank was completely drained at 6:45 pm. If pipe X alone can empty the full tank in 5 hours, while pipe B alone can fill up the empty tank in 4 hours, how long will it take pipe A alone to fill up the empty tank?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
At 1 pm, Poseidon opened pipe A to fill an empty tank with water.
Two hours later, Zeus opened pipe B which also fills the tank, but accidentally opened pipe X which drains the tank.
At 4 pm, evil Hades closed both pipes A and B. With pipe X left open, the tank was completely drained at 6:45 pm.
If pipe X alone can empty the full tank in 5 hours, while pipe B alone can fill up the empty tank in 4 hours, how long will it take pipe A alone to fill up the empty tank?
:
From the information given we know:
Pipe A ran from 1 pm to 4 pm; 3 hrs
Pipe B ran from 3 pm to 4 pm; 1 hr
Pipe x ran from 3 pm to 6:45; 3.75 hrs
:
Let A = time for pipe A to fill the tank by itself
Let a full tank = 1
then
An empty tank = 0:
:
Pipe A + pipe B - pipe x = empty tank
+ - =
multiply by 20A, clear the denominators, resulting in
20(3) + 5A - 4A(3.75) = 0
60 + 5A - 15A = 0
60 - 10A = 0
60 = 10A
A = 160/10
A = 6 hrs to fill the tank alone

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