SOLUTION: If Angela was to paint her living room alone,it would take her 5 hours. Her sister evenlyn could do the job in 7hours.How long would it take them working together??

Two ways to do it, in your head, or by algebra.

1. In your head:  The LCM of 7 hours and 5 hours is 35 hours.  If they worked
together for 35 hours Angela would paint 7 living rooms while Evelyn painted
5 living rooms.  So in those 35 hours they would have painted 12 living rooms.
So to paint just one living room it would take them 1/12th of 35 hours or
35/12ths of an hour.  36 twelfths is 3 hours so 35 twelfths is 1/12 of an hour
or 5 minutes less that 3 hours.  Answer: 2 hours and 55 minutes.   

2. By algebra:

Make this chart:


                        Rooms painted     Time in hours     Rate in rooms/hour
Angelo working alone
Evelyn working alone
Both working together

Let x be the answer, which is the time required for both working together 
to painr 1 room.  So put x for the rime together and 1 for the number 
of rooms.

                        Rooms painted     Time in hours     Rate in rooms/hour
Angelo working alone
Evelyn working alone
Both working together         1                  x

Fill in the times for them to paint 1 room :

                        Rooms painted     Time in hours     Rate in rooms/hour
Angelo working alone          1                  5 
Evelyn working alone          1                  7
Both working together         1                  x

Fill in the rate in rooms/hour by dividing the number of rooms by the number
of hours.

                        Rooms painted     Time in hours     Rate in rooms/hour
Angelo working alone          1                  5                 1/5 
Evelyn working alone          1                  7                 1/7
Both working together         1                  x                 1/x

The equation comes from 

               +  =  

                            +  = 

Multioply by 35x
                         7x + 5x = 35
                             12x = 35
                               x = 
                               x =  hours or 

                        2 hours and 55 minutes.

Edwin