Question 1108519
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<pre>
The first painter makes {{{1/15}}} of the job per day; it is his rate of work.


In three days he did  {{{3/15}}} = {{{1/5}}} of the job;  hence,  {{{4/5}}} of the job remained.


The second painter makes {{{1/10}}} of the job per day; it is his rate of work.


Hence, their combined rate of work is {{{1/10}}} + {{{1/15}}} = {{{3/30}}} + {{{2/30}}} = {{{5/30}}} = {{{1/6}}} of the job per day.


Hence, it will take  {{{((4/5))/((1/6))}}} = {{{(4*6)/5}}} = {{{24/5}}} = {{{4}}}{{{4/5}}} of the day for the two painters to complete the painting.
</pre>

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So, my answer coincides with that by @jomiceli.


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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.