SOLUTION: If a guy can wash a car in 6 minutes by himself and a different guy can wash the car in 8 minutes by himself how long would it take to wash the car together

There are two methods, (1) in your head and (2) by algebra.

(1) In your head.

The LCM of 6 minutes and 8 minutes is 24 minutes.  Working together for 24 minutes, 
washing identical cars, the first guy would wash 4 cars and the second
guy would wash 3 cars.  That's 7 cars in 24 minutes or 1 car in 24/7 or  minutes.

(2)  By algebra.

Make this chart:
                             Number of         No. of      Rate in  
                           cars washed         Minutes     Cars/minute
1st guy washing alone
2nd guy washing alone
Both painting together

Let x be the number of minutes required for both to wash 1 car, so fill in
1 for the number of cars washed by both washing together and x for the
number of minutes.  Also fill in 1 car and 6 and 8 for the numbers of minutes
required for each to wash 1 car separately:

                             Number of         No. of      Rate in  
                           cars washed         Minutes     Cars/minute
1st guy washing alone           1                 6
2nd guy washing alone           1                 8
Both painting together          1                 x

Now fill in the Rates in cars/minute by dividing cars by minutes:

                             Number of         No. of      Rate in  
                           cars washed         Minutes     Cars/minute
1st guy washing alone           1                 6           1/6
2nd guy washing alone           1                 8           1/8
Both painting together          1                 x           1/x


                     The equation comes from

       +  = 

                     +  = 

 Multiply through by 24x
                  
                    4x + 3x = 24
                         7x = 24
                          x =  =  minutes.

Edwin