SOLUTION: Alvin and Lito washed the family car in 18 minutes. When each washed the car alone, Lito took 15 minutes longer to do the job than Alvin. How long did it take Alvin to washed the

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 !