SOLUTION: 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

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    part of the entire job, working alone;

             Jay makes    part of the entire job, working alone.


Working together, they make    of the job in one hour.


It gives an equation


     +  = .       (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 ANSWER to the problem:


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


CHECK.    +  =  =  =  = .   !  Correct.  Equation (1)  is held  !