Question 1206762
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A and B together can complete a work in 12 days.
C alone can complete the same work in 20 days. B alone can complete the same work in 18 days.
How many days will it take to do the same work if A and C does it together?
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<pre>
A and B combined rate of work is  {{{1/12}}}  of the job per day.

B's individual rate of work is  {{{1/18}}}  of the job per day.


Hence, A's individual rate of work is the difference  

    {{{1/12}}} - {{{1/18}}} = {{{3/36}}} - {{{2/36}}} = {{{1/36}}}.


In other words,  A can do  {{{1/36}}}  of the job per day, working alone.


Hence, A and C combined rate of work is

    {{{1/36}}} + {{{1/20}}} = {{{5/180}}} + {{{9/180}}} = {{{14/180}}}  of the job per day.


Hence, A and C will complete the job in  {{{180/14}}} = {{{90/7}}} days = 12{{{6/7}}}  days.    <U>ANSWER</U>
</pre>

Solved.


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It is a standard and 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.