SOLUTION: Martha can rake the leaves in her yard in 5 hours. Her younger brother can do the job in 6 hours How long will it take if they work together?

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Question 76730: Martha can rake the leaves in her yard in 5 hours. Her younger brother can do the job in 6 hours How long will it take if they work together?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

Martha can rake the leaves in her yard in 5 hours. 
Her younger brother can do the job in 6 hours 
How long will it take if they work together?

Martha can rake the leaves in her yard in 5 hours.
So in ONE hour, she can rake 1/5th of the leaves.
Therefore in x hours, she can rake x/5ths of the leaves.

Her younger brother can do the job in 6 hours
So in ONE hour, he can rake 1/6th of the leaves.
Therefore in x hours, he can rake x/6ths of the leaves.

The fraction of the leaves Martha rakes +
  The fraction of the leaves her younger brother rakes =
    1 yardful of leaves

             x/5 + x/6 = 1

Multiply through by LCD, which is 30

      30(x/5)+ 30(x/6) = 30(1)

               6x + 5x = 30

                   11x = 30

                     x = 30/11 

                     x = 2 8/11

                     x = 2 hr, 43 mins, 38 2/11 sec.

Edwin
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