Question 280398
Jack usually mows his lawn in 3 hours. Jill can mow the same yard in 4 hours. How much time would it take for them to mow the yard together?

The amount of lawn mowed is the product of the rate of mowing and the elapsed time (i.e. m = r*t).

Jack's rate of mowing is 1/3. Jill's ratre is 1/4.  So their combines rate of mowing is 1/3 + 1/4. Let t be the ime needed. Then we have for mowing 1 lawn:

1 = (1/3 + 1/4)*t 
1 = (4/12 + 3/12)*t
1 = (7/12)*t
t = 1/(7/12) 
t = 1*(12/7)
t = 12/7 hours