SOLUTION: It takes Johnny 4 hours to mow the lawn. It takes Rebecca 3 hours to mow the same lawn. How long would it take if they worked together? I cannot figure out the formula to use to

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Question 148046: It takes Johnny 4 hours to mow the lawn. It takes Rebecca 3 hours to mow the same lawn. How long would it take if they worked together?
I cannot figure out the formula to use to determine this. I keep trying to make 4 and 3 hours equal 1 (lawn). Just not sure where to begin. If I had the formula... thank-you.
Found 3 solutions by checkley77, edjones, scott8148:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website!
THE FORMULA FOR THIS PROBLEMS IS:
J*R/(J+R)
4*3/(4+3)
12/7=1.714 HOUR TO COMPLETE THE JOB WORKING TOGETHER.

Answer by edjones(8007)   (Show Source):
You can put this solution on YOUR website!
Johnny can do 1/4 the job in 1 hr.
Rebbecca can do 1/3 the job in 1 hr.
1/4 + 1/3
=(3+4)/12
=7/12 of the job in 1 hr together.
12/7 hr. Time it takes both of them to do the job.
.
Ed

Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website!
when people work together on a task, they each do some FRACTION of the whole task

since working together takes less time than working alone
__ the combined time divided by an individual's time equals the fraction of the task that the individual completes

eg. Bill can do a task in 9 hours __ when he works with a group, the task takes 3 hours
__ Bill does 1/3 (3/9) of the task

let x="time together" __ (x/4)+(x/3)=1 __ 1 is the whole task, the sum of the fractions

multiplying by 12 (LCD) __ 3x+4x=12 __ combining terms __ 7x=12 __ dividing by 7 __ x=12/7