Question 1058038
.
Jack and Jill together can do a piece of work in 3 days. 
They can finish the work if Jack works for 2 days and Jill 
works for 4 days. Find the time required for each to do the 
work.
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<pre>
Since "Jack and Jill together can do a piece of work in 3 days", they do {{{1/3}}} of the job working together.

The next phrase of the condition says:
    "They can finish the work if Jack works for 2 days and Jill works for 4 days."

You can re-phrase it in this equivalent way:
    They can finish the work if Jack and Jill work together for 2 days and then Jill works for additional 2 days.


OK, very good.
But then, working 2 days together, Jack and Jill will do {{{2/3}}} of the job.

It means that Jill can complete the remaining {{{1/3}}} of the job in two days.
Hence, Jill can complete the entire job in 6 days.


    Half of the problem is just solved. Now we can easily complete the rest, too.


Since Jill does the entire job in 6 days, in three days she makes {{{1/2}}} of the job.
It means that in 3 day Jack makes the remaining {{{1/2}}} of the job.
In turn, it means that Jack can do the entire work in 6 days.
</pre>

Solved.



<U>The lesson to learn from this solution</U>: 


&nbsp;&nbsp;&nbsp;&nbsp; There is no need to solve equations.
&nbsp;&nbsp;&nbsp;&nbsp; You can solve it using simple logic.
&nbsp;&nbsp;&nbsp;&nbsp; You also are supposed to operate freely with fractions. That's all.


&nbsp;&nbsp;&nbsp;&nbsp; Simple logic and fractions.


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There is a bunch of lessons on similar joint-work problems with detailed explanations 

&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>".