Question 807710
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<pre>
Let x be the rate of the largest pipe.


Then, according to the condition, the rate of the smallest pipe is {{{x/3}}},  while the rate of the medium pipe is {{{x/2}}} of the tank volume per hour.


The equation is 

{{{x}}} + {{{x/2}}} + {{{x/3}}} = {{{1/3}}},   or

{{{(6x)/6}}} + {{{(3x)/6}}} + {{{(2x)/6}}} = {{{1/3}}},

{{{(6x + 3x + 2x)/6}}} = {{{1/3}}}  ====>  Multiply both sides by 6  ====>

6x + 3x + 2x = 2  ====>  11x = 2  ====>  x = {{{2/11}}}.


Thus the largest pipe will fill the tank in {{{11/2}}} = 5.5 hours.


Then the smallest pipe will fill it in 5.5*3 = 16.5 hours, and
     the medium   pipe will fill it in 5.5*2 = 11 hours.
</pre>

<U>Answer</U>.  &nbsp;5.5 &nbsp;hours for the largest pipe;  &nbsp;&nbsp;16.5 &nbsp;hours for the smallest pipe;  &nbsp;&nbsp;and &nbsp;11&nbsp; hours for the medium pipe.



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It is a typical joint work problem.


There is a wide variety of similar solved joint-work problems with detailed explanations in this site. &nbsp;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>" &nbsp;of the section &nbsp;"<U>Word problems</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.