Question 1129779
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<pre>
Let x be the time for pipe C to empty the tank.


Then the time for the pipe B to fill the tank is (x+2) hours.


The rate of work for pipes A, B and C are  {{{1/5}}},  {{{1/(x-2)}}} and  {{{-1/x}}} of the tank volume per hour.


The balance equation is


    {{{1/5}}} + {{{1/(x-2)}}} - {{{1/x}}} = {{{1/3}}},    or

    {{{1/(x-2)}}} - {{{1/x}}} = {{{1/3 - 1/5}}} = {{{5/15-3/15}}} = {{{2/15}}}.


To solve it, multiply both sides by  15*x*(x-2)  and simplify step by step.  You will get


    15x - 15*(x-2) = 2x*(x-2)

    30 = 2x^2 - 4x

    2x^2 - 4x - 30 = 0

    x^2 - 2x - 15 = 0

    (x-5)*(x+3) = 0


<U>Answer</U>.  x = 5 hours.


<U>Check</U>.  {{{1/5}}} + {{{1/(5-2)}}} - {{{1/5}}} = {{{1/3}}}  of the tank volume.   ! Correct !
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To see many other similar solved problems, &nbsp;look into 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.