Question 1075948
.
The formal solution is THIS:


<pre>
Jane makes {{{1/40}}} of the job per minute.

Janes makes {{{1/35}}} of the job per minute.


Working together, they make {{{1/40 + 1/35}}} = {{{14/560 + 16/560}}} = {{{30/560}}} = {{{3/56}}} of the job per minute.


Hence, they will complete the job in {{{56/3}}} minutes = {{{18}}}{{{2/3}}} minutes = 18 minutes and 40 seconds.
</pre>

I call this solution "formal", since I assume (without a proof; as granted) that their rates can be summed in this job.



For a wide variety of similar solved joint-work problems with detailed explanations 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> 

in this site.


Read them and get be trained in solving joint-work problems.


Also, 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>" of the section "<U>Word problems</U>".