Question 1138481
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<pre>
Let x be the time for the faster computer to do the job working alone (in minutes).

Then the time for slower compute is (x+5) minutes, according to the condition.


Then their individual rates are {{{1/x}}}  and  {{{1/(x+5)}}}, giving the combined rate equal to the sum of individual rates.


It gives you an equation


    {{{1/x}}} + {{{1/(x+5)}}} = {{{1/6}}}


To solve it, multiply both sides by 6x*(x+5). You will get


    6(x+5) + 6x =  x*(x+5)

    6x + 30 + 6x = x^2 + 5x

    x^2 - 7x - 30 = 0

    (x-10)*(x+3) = 0


The roots are 10 and -3, and only positive root is meaningful.


<U>Answer</U>.  The faster computer makes this job in 10 minutes, working alone.


<U>CHECK</U>.   {{{1/10}}} + {{{1/(10+5)}}} = {{{1/10}}} + {{{1/15}}} = {{{3/30 + 2/30}}} = {{{5/30}}} = {{{1/6}}}.   ! Correct !
</pre>

Solved.


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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. 
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> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Using-quadr-eqns-to-solve-word-problems-on-joint-work.lesson>Using quadratic equations to solve word problems on joint work</A> &nbsp;(*)


Of this list, &nbsp;the most relevant problems are in the lesson marked by &nbsp;(*).

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.