SOLUTION: Mary can paint a house in 4 hours. John can paint a house in 6 hours. How long will it take for them to paint a house together

Make this chart:
                       number of       number of        rate
                        houses           hours           in
                        painted         required     houses/hour
Mary painting alone      
John painting alone
Both painting together 

Let x = the number of hours it will take both painting together.
Fill that in and the number of hours required for Mary and John, 4 and
6 respectively.

                       number of       number of        rate
                        houses           hours           in
                        painted         required     houses/hour
Mary painting alone                        4 
John painting alone                        6
Both painting together                     x



In each case 1 house is painted. We fill in 1 for the number of houses
painted in each case:

                       number of       number of        rate
                        houses           hours           in
                        painted         required     houses/hour
Mary painting alone        1               4
John painting alone        1               6
Both painting together     1               x

Fill in the rates in houses/hour bu dividing the number of houses
by the number of hours required.

                       number of       number of        rate
                        houses           hours           in
                        painted         required     houses/hour
Mary painting alone        1               4             1/4 
John painting alone        1               6             1/6
Both painting together     1               x             1/x

                        
The equation comes from:

                    +  =    

                        +  = 


Solve that and get x = 2.4 hours or 2 hours 24 minutes

Edwin