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
