<PRE><B>Question 1197196</B>
.
Janet can do a job in 3 hours while Gary can do the same job in 2 hours. 
If Janet works for an hour before Gary helps her, how long will it take 
for them to finish the job together?
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&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;Solve it mentally, &amp;nbsp;without using equations - and have fun.



&lt;pre&gt;
Working 1 hour alone, Janet completed 1/3 of the job; hence, 2/3 of the job remained.


Janet&#39;s rate of work is  1/3  of the job per hour.

Gary&#39;s  rate of work is  1/2  of the job per hour.


Their combined rate of work is  {{{1/3 + 1/2}}} = {{{2/6 + 3/6}}} = {{{5/6}}}  of the job per hour.


Hence, working together, they complete the remaining  2/3  of the job in

    {{{((2/3))/((5/6))}}} = {{{(2*6)/(3*5)}}} = {{{(2*2)/5}}} = {{{4/5}}}  of an hour = 48 minutes.


&lt;U&gt;ANSWER&lt;/U&gt;.  Working together, they complete the remaining  2/3  of the job in 48 minutes.
&lt;/pre&gt;

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. &amp;nbsp;See the lessons

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Word-problems-WORKING-TOGETHER-by-Fractions.lesson&gt;Using Fractions to solve word problems on joint work&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Solving-more-complicated-word-problems-on-joint-work.lesson&gt;Solving more complicated word problems on joint work&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Selected-problems-from-the-archive-on-joint-work-word-problems.lesson&gt;Selected joint-work word problems from the archive&lt;/A&gt; 



Read them and get be trained in solving joint-work problems.


Also, &amp;nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson&gt;ALGEBRA-I - YOUR ONLINE TEXTBOOK&lt;/A&gt;.


The referred lessons are the part of this textbook under the topic 
&quot;&lt;U&gt;Rate of work and joint work problems&lt;/U&gt;&quot; &amp;nbsp;of the section &amp;nbsp;&quot;&lt;U&gt;Word problems&lt;/U&gt;&quot;.



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.



</PRE>