Let x be the time in minutes for Alvin to wash the car alone.

Then the time for Lito to wash the car alone is (x+15) minutes, according to the condition.


So, in one minute Alvin makes    of the job, working alone;

                  Lito  makes    of the job, working alone.


Thus, working together, they make   +   of the job,

and this combined rate of work is equal to  ,  according to the condition.


So, we have this equation to find x

     +  = .     (*)


At this point, the setup is just completed.  Equation (*) is your governing equation to find x.

Equation (*) says that the combined rate of work is equal to the given value.


To solve equation (*), multiply both siodes by 18*x*(x+15}}}.  You will get

    18*(x+15) + 18x = x*(x+15).


Simplify it step by step.


    18x + 270 + 18x = x^2 + 15x

    36x + 270 = x^2 + 15x

    x^2 + 15x -36x - 270 = 0

    x^2 - 21x - 270 = 0.


Fortunately, the left side admits factoring

    (x-30)*(x+9) = 0.


So, this equation has two different roots, x= 30 and x= -9.

Of them, only the root x= 30 is meaningful.


So, Alwin can complete the job in 30 minutes, working alone;  Lito can do it in 30+15 = 45 minutes.    ANSWER


CHECK.   +  =  +  =  = .     ! Correct !