Question 1185232
.
Joe can paint a room in 6 hours less time than Jay. If they can paint the
room in 4 hours working together, how long would it take each to paint
the room working alone
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<pre>
Let x be the time for Joe to complete the job alone, in hours;

then the time for Jay is (x+6) hours.


In one hour, Joe makes  {{{1/x}}}  part of the entire job, working alone;

             Jay makes  {{{1/(x+6)}}}  part of the entire job, working alone.


Working together, they make  {{{1/4}}}  of the job in one hour.


It gives an equation


    {{{1/x}}} + {{{1/(x+6)}}} = {{{1/4}}}.       (1)


It is your basic equation.  As soon as you get it, the setup is done.


To solve the equation, multiply both sides by  4x*(x+6)  and simplfy.   You will get


    4(x+6) + 4x = x^2 + 6x

    x^2 - 2x - 24 = 0.


Factor left side


    (x-6)*(x+4) = 0.


Of two roots,  x= 6  and  x= 4, only positive x= 6 is meaningful.


It gives the <U>ANSWER</U> to the problem:


    Joe con make the entire work in 6 hours, working alone;  Jay can do it in 6+6 = 12 hours.


<U>CHECK</U>.   {{{1/6}}} + {{{1/(6+6)}}} = {{{1/6 + 1/12}}} = {{{2/12 + 1/12}}} = {{{3/12}}} = {{{1/4}}}.   !  Correct.  Equation (1)  is held  !
</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. &nbsp;See the lesson

&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> 


Read it 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 lesson is 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.