Question 1052907
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A AND B WORKING TOGETHER TAKE 8 AND 18 LESS DAYS THAN A ALONE AND B ALONE RESPECTIVELY TO DO A WORK. 
THE NUMBER OF DAYS TAKEN BY A AND B WORKING TOGETHER TO DO THE WORK IS?
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<pre>
Let x = THE NUMBER OF DAYS TAKEN BY A AND B WORKING TOGETHER TO DO THE WORK.

The the number of days for A to do the job working alone is (x+8), and 
    the number of days for B to do the job working alone is (x+18).


Then the standard equation for joint work is

{{{1/(x+8) + 1/(x+18)}}} = {{{1/x}}}.

To solve it, multiply everything by x*(x+8)*(x+18). You will get

x*(x+18) + x*(x+8) = (x+8)*(x+18).

Simplify:

{{{x^2 + 18x + x^2 + 8x}}} = {{{x^2 + 8x + 18x + 144}}},  or

{{{x^2}}} = 144.

Hence, x = {{{sqrt(144)}}} = 12.

<U>Answer</U>.  12 days.
</pre>

A wide variety of similar joint-work problems were solved with detailed explanations in 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> 

in this site.


Read them and become an expert 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>".



As a concluding remark, ignore writing by the other tutor, named "josgarithmetic".
The way he proposes is the way to nowhere.