Question 1072941
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<pre>
Let P be the rate of the pipe (in the unit "tank volume per hour").
Let L be the rate of the leak (in the same unit).


Then you have two equations:

P - L = {{{1/10}}}    (1)   (The pipe fills the tank in 10 hours, when the leak is in action).

P = {{{1/8}}}.        (2)   ("The pipe can fill a water tank in 8 hours.")


Substitute (2) into equation (1). You will get

{{{1/8}}} - L = {{{1/10}}}  --->  L = {{{1/8 - 1/10}}} = {{{5/40-4/40}}} = {{{1/40}}}.


So, due to the leak, amount of water of {{{1/40}}} of the tank volume goes out.

It means, that the full tank will become empty in 40 hours due to the leak.
</pre>

Solved.



It is a typical joint work problem.


For a wide variety of similar solved joint-work problems with detailed explanations 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> 

in this site.


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

&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>".