SOLUTION: Fred can paint a house in 12 hours and George can paint the same house in 14 hours. How long does it take Fred and George to paint the house together?

Question 1025133: Fred can paint a house in 12 hours and George
can paint the same house in 14 hours. How long
does it take Fred and George to paint the house
together?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
Fred can paint a house in 12 hours and George
can paint the same house in 14 hours. How long
does it take Fred and George to paint the house
together?

Fred's painting rate 1 house per 12 hours plus 
George's rate of 1 house per 14 hours gives 
their combined rate as

1/12 + 1/14 = 7/84+6/84 = 13/84ths of a house 
per hour.  Let this equal to 1 house per x hours, 
so

1/x = 13/84

Taking reciprocals of both side

x = 84/13 = 6 6/13 hours.

Edwin

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