Question 1149556
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<pre>

Barbara makes  {{{1/4}}}  of the job per hour.


Sarah   makes  {{{1/5}}}  of the job per hour.


Workin together, the sisters make  {{{1/4}}} + {{{1/5}}} = {{{5/20}}} + {{{4/20}}} = {{{9/20}}} of the job per hour.


It means, that the can complete the job in  {{{20/9}}} = {{{2}}}{{{2/9}}} hours, working together.
</pre>

Solved.



This method requires making manipulations with fractions, only.
It does not require solving equation.


If you want or if you need to solve it using equation/equations, do it as follows.



<pre>
Let "t" be the time for two to complete the job, in hours.


Barbara makes  {{{1/4}}}  of the job per hour --- hence, she will make  {{{t/4}}}  of the job in "t" hours.


Sarah makes  {{{1/5}}}  of the job per hour --- hence, she will make  {{{t/5}}}  of the job in "t" hours.


Since they completes the entire work in t hours,

    {{{t/4}}} + {{{t/5}}} = 1.


Multiply both sides by 4*5. You will get

    5t + 4t = 20,

    9t      = 20

     t      = {{{20/9}}}  hours,   the same <U>ANSWER</U>
</pre>

Now you know two basic ways to solve this problem.


------------------------


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. &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>" &nbsp;of the section &nbsp;"<U>Word problems</U>".



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.