Question 635869
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?

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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 

              {{{(matrix(4,1,

"Angelo's",rate,working,alone))}}} + {{{(matrix(4,1,

"Evelyn's",rate,working,alone))}}} = {{{(matrix(5,1,

their,combined,rate,working,together))}}} 

                           {{{1/5}}} + {{{1/7}}} = {{{1/x}}}

Multioply by 35x
                         7x + 5x = 35
                             12x = 35
                               x = {{{35/12}}}
                               x = {{{2&1/12}}} hours or 

                        2 hours and 55 minutes.

Edwin</pre>