SOLUTION: An intake pipe to a reservoir is controlled by a valve which automatically closes when the reservoir is full and opens again when 4/5's of water had been drained off. The intake pi

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Question 1080508: An intake pipe to a reservoir is controlled by a valve which automatically closes when the reservoir is full and opens again when 4/5's of water had been drained off. The intake pipe can fill the reservoir in 4 hours and the outlet pipe can drain it in 10 hours. If the outlet pipe remains open, how much time elapses between the two instants that the reservoir is fill?
Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
An intake pipe to a reservoir is controlled by a valve which automatically closes when the reservoir is full and opens again when 4/5's of water had been drained off.
The intake pipe can fill the reservoir in 4 hours and the outlet pipe can drain it in 10 hours.
If the outlet pipe remains open, how much time elapses between the two instants that the reservoir is fill?
:
let the full tank = 1
From the full position, the outlet pipe will drain 4/5 of the water in: 4%2F5*10 = 8 hrs
At this point the intake pipe comes on which can refill it in 4%2F5*4 = 3.2 hrs but the drain is still on therefore
let t = time for the tank to filled under these conditions
t%2F3.2 - t%2F8 = 1
multiply by 64, cancel the denominators
20t - 8t = 64
12t = 64
t = 64/12
t = 51%2F3 hrs
Plus the 8 hrs to drain off 4/5 of water.
131%2F3 hr

Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
An intake pipe to a reservoir is controlled by a valve which automatically closes when the reservoir is full and opens again
when 4/5's of water had been drained off. The intake pipe can fill the reservoir in 4 hours and the outlet pipe can drain it in 10 hours.
If the outlet pipe remains open, how much time elapses between the two instants that the reservoir is fill?
~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

1.  How long will it take to drain the full reservoir to the level of 1%2F5 if only outlet pipe works?


    Very easy. The rate of the outlet pipe is 1%2F10 of the tank volume per hour,
   therefore, it will take %28%284%2F5%29%29%2F%28%281%2F10%29%29 = %284%2A10%29%2F5 = 8 hours.



2.  How long will it take to fill the reservoir from the level of 1%2F5 if both inlet and outlet pipes works?

    The combined rate of filing in this case is 1%2F4+-+1%2F10 = 5%2F20+-+2%2F20 = 3%2F20 of the tank volume per hour.

    Therefore, the filling at these conditions will take %28%284%2F5%29%29%2F%28%283%2F20%29%29 = %284%2A20%29%2F%285%2A3%29 = 80%2F15 = 55%2F15 hours = 51%2F3 hours = 5 hours and 20 minutes.



3.  The entire process, consisting of draining and filling, will take 8 hours + 5 hours and 20 minutes = 13 hours and 20 minutes.


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