Question 1073931
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Let x be the time for the large pipe to fill the tank working alone, in minutes.
Then the time for the small pipe to fill the tank working alone is (t+8) minutes.


The larger pipe fills {{{1/x}}} of the tank volume per minute.

The smaller pipe fills {{{1/(x+8)}}} of the tank volume per minute.

The two pipes fill {{{1/x + 1/(x+8)}}} of the tank volume, working simultaneously.

The condition says 

{{{3/x + 3/(x+8)}}} = 1. 

--->  3*(x+8) + 3x = x*(x+8)  --->  {{{x^2 + 2x - 24}}} = {{{0}}}  --->  (x-6)*(x+4) = 0  ---->

the only positive root is t= 6 minutes.


<U>Answer</U>.  6 minutes for the large pipe to fill the tank, and 6 + 8 = 14 minutes for the small pipe.
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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>".