SOLUTION: A tank has a supply pipe and an exhaust pipe. The exhaust pipe takes 5 minutes longer to empty the tank for the supply pipe to fill it. If both are open, it takes the supply pipe 3
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-> SOLUTION: A tank has a supply pipe and an exhaust pipe. The exhaust pipe takes 5 minutes longer to empty the tank for the supply pipe to fill it. If both are open, it takes the supply pipe 3
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Question 90946: A tank has a supply pipe and an exhaust pipe. The exhaust pipe takes 5 minutes longer to empty the tank for the supply pipe to fill it. If both are open, it takes the supply pipe 30 minutes to fill the tank. Find how long it takes the supply pipe to fill the tank when the exhaust pipe is closed. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A tank has a supply pipe and an exhaust pipe. The exhaust pipe takes 5 minutes longer to empty the tank for the supply pipe to fill it. If both are open, it takes the supply pipe 30 minutes to fill the tank. Find how long it takes the supply pipe to fill the tank when the exhaust pipe is closed.
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Let T = time (in min) for the supply pipe to fill the tank by itself (no exhaust)
Then
(T+5) = time for the exhaust pipe to empty a full tank by itself (no supply)
:
Let the full tank = 1:
:
Let the one filling the tank be +, and the one draining the tank be -
: - = 1
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Multiply equation by T(T+5) to eliminate the denominators, then you have:
30(T+5) - 30T = T(T+5)
:
30T + 150 - 30T = T^2 + 5T; note the 30t's will cancel
:
T^2 + 5T - 150 = 0; a quadratic equation
Factors to:
(T+15)(T-10) = 0
:
T = +10 min, positive solution is what we want here.
:
:
Check:
30/10 - 30/15 =
3 - 2 = 1 (a full tank)
:
Did this make sense to you? Any questions?
