Question 1088683
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A postal worker can sort a day's worth of mail in 8 hours. With her supervisor helping, it takes 3 hours. 
How long would it take the supervisor working alone?
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<pre>
Since the worker and the supervisor can complete the work i n 3 hours, their combined rate of work is {{{1/3}}} of the work per hour.


The worker's individual rate of work is {{{1/8}}} of the work per hour.


Hence, the supervisor's rate of work is the difference {{{1/3 - 1/8}}} = {{{8/24 - 3/24}}} = {{{5/24}}} of the work per hour.


It means that the supervisor can complete the work in {{{1/((5/24))}}} hours, which is equal to {{{24/5}}} = {{{4}}}{{{4/5}}} hours = 4 hours and 48 minutes.
</pre>

<U>Answer</U>. the supervisor can complete the work in 4 hours and 48 minutes, if he will work alone.



Solved.



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