Question 1041342
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Tom paints a fence in 4 hours.Huck paints the fence in 6 hours. How long does it take for them to paint the fence working together?
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<pre>
Tom paints {{{1/4}}} of the fence length in one hour (in each hour).
It is his rate of work.

Huck paints {{{1/6}}} of the fence length in one hour (in each hour).
It is Huck's rate of work.

When the both work together, they paint {{{1/4 + 1/6}}} = {{{3/12 + 2/12}}} = {{{5/12}}} of the fence length in one hour. In each hour.

So, their combined rate of work is the sum of the individual rates and is equal to {{{5/12}}} of the fence length per hour.

It means that the both will complete their job in {{{12/5}}} of an hour.

{{{1/5}}} of an hour is 12 minutes. {{{12/5}}} of the hour is 12*12 = 144 minutes, or 2 hours and 24 minutes.

<U>Answer</U>.  Both boys will complete the job in 2 hours and 24 minutes.
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On solving joint work problems see the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Rate-of-work-problem.lesson>Rate of work problems</A>,

&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.