Question 1199268
.
Jay can do a painting job in 2/3 as many days as Chris can, 
and Chris can do it in 3/4 as many days as Araceli can. 
If all three work together, they can do it in 36/13 days. 
In how many days can each of them alone do the work?
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<pre>
Let "a" be the Araceli's rate of work.


Then Chris' rate of work is  {{{(4/3)a}}}, and Jay's rate of work is {{{(3/2)a}}}.


Their combined rate of work is then 

    a + {{{(4/3)a}}} + {{{(3/2)*(4/3)a}}} = a + {{{(4/3)a}}} + 2a = {{{(3a + 4a + 6a)/3}}} = {{{(13/3)a}}}.


From the other side, their combined rate of work is  {{{13/36}}}.


It gives us this equation

    {{{(13/3)a}}} = {{{13/36}}}.


From this equation,  a = {{{1/12}}}.


Thus Araceli can make the job in 12 days, working alone; Cris can make it in  {{{(3/4)*12}}} = 9 days
and Jay can make it in  {{{(2/3)*9}}} = 6 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.


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.