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?
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<pre>
1.  How long will it take to drain the full reservoir to the level of {{{1/5}}} if only outlet pipe works?


    Very easy. The rate of the outlet pipe is {{{1/10}}} of the tank volume per hour,
   therefore, it will take {{{((4/5))/((1/10))}}} = {{{(4*10)/5}}} = 8 hours.



2.  How long will it take to fill the reservoir from the level of {{{1/5}}} if both inlet and outlet pipes works?

    The combined rate of filing in this case is {{{1/4 - 1/10}}} = {{{5/20 - 2/20}}} = {{{3/20}}} of the tank volume per hour.

    Therefore, the filling at these conditions will take {{{((4/5))/((3/20))}}} = {{{(4*20)/(5*3)}}} = {{{80/15}}} = {{{5}}}{{{5/15}}} hours = {{{5}}}{{{1/3}}} 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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There is a wide variety of solved joint-work problems with detailed explanations in this site. See the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Word-problems-WORKING-TOGETHER-by-Fractions.lesson>Using Fractions to solve word problems on joint work</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Solving-more-complicated-word-problems-on-joint-work.lesson>Solving more complicated word problems on joint work</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Selected-problems-from-the-archive-on-joint-work-word-problems.lesson>Selected joint-work word problems from the archive</A> 



Read them and get be trained in solving joint-work problems.


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The referred lessons are the part of this textbook under the topic "<U>Rate of work and joint work problems</U>" of the section "<U>Word problems</U>".