SOLUTION: Both inlet and outlet pipes to a cider barrel were mistakenly left open. Nevertheless, the barrel filled in 12 hours. With only the outlet pipe open, a full barrel of cider can be

Question 532541: Both inlet and outlet pipes to a cider barrel were mistakenly left open. Nevertheless, the barrel filled in 12 hours. With only the outlet pipe open, a full barrel of cider can be emptied in 1 hour more than the time to fill an empty barrle with only the inlet pipe open. How long would draining a full barrel of cider take with the outlet pipe open and the inlet pipe closed?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Both inlet and outlet pipes to a cider barrel were mistakenly left open.
Nevertheless, the barrel filled in 12 hours.
With only the outlet pipe open, a full barrel of cider can be emptied in 1 hour more than the time to fill an empty barrel with only the inlet pipe open.
How long would draining a full barrel of cider take with the outlet pipe open and the inlet pipe closed?
:
Let t = time required by the outlet pipe with inlet closed, to drain the barrel
then
(t-1) = time required by the inlet pipe to fill the barrel (outlet closed)
:
let a full tank = 1
:
- = 1
multiply by t(t-1) to clear the denominators, results:
12t - 12(t-1) = t(t-1)
12t - 12t + 12 = t^2 - t
Arrange as a quadratic equation
0 = t^2 - t - 12
Factors to
(t-4)(t+3) = 0
the positive solution is all we want here
t = 4 hrs to drain the tank with the inlet closed
:
:
- =
4 - 3 = 1
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