Martha can rake the leaves in her yard in 7 hours. Her brother can do the job in 4 hours. How long will it take them to do the job working together?

Question

Martha can rake the leaves in her yard in 7 hours. Her brother can do the job in 4 hours.
How long will it take them to do the job working together?

Answer 1

It is helpful to think about the problem this way:

In one hour, Martha can rake 1/7 of the yard
In one hour, brother can rake 1/4 of the yard

So let x be the number of total hours needed to rake the yard:

x*1/7 + x*1/4 = 1 (or the whole yard)
x/7 + x/4 = 1
4x +7x = 28
11x = 28
x = 28/11 hours, or 2 and 6/11 hours, and 6/11 of an hour is approx. 33 minutes

So together they can do the yard in 2 hours and 33 minutes.

Hope that helps!