Question 1084102
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<pre>
The rate of filling the inflatable pool with the electrical pump is {{{1/22}}} of the volume per minute.


The rate of rejecting the air through the open valve is 1/52 of the pool volume per minute.


The combined rate is the difference {{{1/22-1/52}}} = {{{52/(22*52) - 22/(22*52)}}} = {{{30/(22*52)}}} = 0.0262 of the pool volume per minute.


Hence it will take {{{1/0.0262}}} = 38.133 minutes to fill the pool if the electrical pump is ON and the pool's valve is accidentally open.
</pre>

Solved with all step explained.



It is a typical joint-work problem.


There is a wide variety of similar 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.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


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>".



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<U>Comment from student</U>: No, I don't understand still. Could you give more steps to get the answer? 
I'm working this in an ACT math book, so I already have the answer, I just need to have the steps to GET to the answer.
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<U>My response</U>. I got this comment/feedback, &nbsp;but I am not sure if it relates to this problem, since there is no reference to the problem ID
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(which, actually, MUST be . . . )


If it is not your comment, then ignore my response.


But if it is yours, then read it attentively.


<pre>
    You got <U>THE BEST POSSIBLE SOLUTION AND EXPLANATION</U>.


    <U>READ AND RE-READ</U> it <U>UNTIL</U> you will get <U>FULL UNDERSTANDING</U>.


    <U>ALSO READ AND RE-READ the lessons I referred to</U>.
</pre>

If you still do not understand it, it means that you are in wrong class.



I wait the feedback from you with your "Thanks . . . " when you get understanding.