.
The rate of filling the inflatable pool with the electrical pump is 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 = = = 0.0262 of the pool volume per minute.
Hence it will take = 38.133 minutes to fill the pool if the electrical pump is ON and the pool's valve is accidentally open.
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
- Using Fractions to solve word problems on joint work
- Solving more complicated word problems on joint work
- Selected joint-work word problems from the archive
Read them and get be trained in solving joint-work problems.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".
-------------
Comment from student: 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.
-------------
My response. I got this comment/feedback, but I am not sure if it relates to this problem, since there is no reference to the problem ID
(which, actually, MUST be . . . )
If it is not your comment, then ignore my response.
But if it is yours, then read it attentively.
You got THE BEST POSSIBLE SOLUTION AND EXPLANATION.
READ AND RE-READ it UNTIL you will get FULL UNDERSTANDING.
ALSO READ AND RE-READ the lessons I referred to.
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.