SOLUTION: Jack mows the lawn in 3 hours. Jane mows the same yard in 4 hours. If they worked together how much time would it take them to mow the yard?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Jack mows the lawn in 3 hours. Jane mows the same yard in 4 hours. If they worked together how much time would it take them to mow the yard?      Log On


   



Question 314417: Jack mows the lawn in 3 hours. Jane mows the same yard in 4 hours. If they worked together how much time would it take them to mow the yard?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = time it takes them to mow the yard working together. This means that in 1 hour, Jack can mow 1/3 of the yard, Jane can mow 1/4 of the yard, and working together, they can do 1/x of the yard.

The equation is
1%2F3%2B1%2F4=1%2Fx

The LCD is 12x, so multiply both sides of the equation by 12x
12x%2A%281%2F3%29%2B12x%2A%281%2F4%29=12x%2A%281%2Fx%29
4x%2B3x=12
7x=12
x=12%2F7 hours (a little less than 2 hours working together.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus