Question 1132152
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<pre>
Dan     makes  {{{1/30}}}  of the entire job per hour.  It is his rate of work.


Ellen   makes  {{{1/40}}}  of the entire job per hour.  It is her rate of work.


Francis makes  {{{1/60}}}  of the entire job per hour.  It is his (or her (?) ) rate of work.


Working together, the tree persons make  {{{1/30 + 1/40 + 1/60}}} = {{{4/120 + 3/120 + 2/120}}} = {{{9/120}}} = {{{3/40}}}  of the entire job per hour.

    It is their COMBINED rate of work, which is the sum of the individual rates.



To solve the problem using one variable, introduce t as the time it takes them to complete the entire job working together.


Then your equation is  <U>Time*Rate</U> = <U>the entire job</U>,  or


    {{{t*(13/40)}}} = 1,


which implies


    t = {{{1/((13/40))}}} = {{{40/3}}} = {{{13}}}{{{1/3}}} hours = 13 hours and 20 minutes.    <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.