SOLUTION: Sam can mow a lawn in 20 minutes and Robert can mow the same lawn in 30 minutes. If they worked together, how long would it take them to do the work? I need the rate of work (R)

Question 248810: Sam can mow a lawn in 20 minutes and Robert can mow the same lawn in 30 minutes. If they worked together, how long would it take them to do the work?
I need the rate of work (R), the time of work (T) , and the work done (W)
the equation is RT = W.
It would help if I am provided a detailed explanation
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The critical insight is that you have to get the equations in terms of accomplishing 1 job.
.
Sam can do the job in 20 min. So he can do the whole job at the rate of 1 job in 20 minutes.
So he does 1/20 of the job per minute.
.
Rob can do the job in 30 min. His rate is 1/30 of the job per minute.
.
Working together how does it take?
.
1/20*x + 1/30*x = 1 job done
, where x = minutes.
.
Multiply everything by 60 go get rid of the fractions.
3x + 2x = 60
5x = 60
.
Divide both sides by 12
x = 12
.
So our candidate answer is working together it will take them 12 minutes.
.
Let's check.
In 12 minutes, Sam does 12/20 of the job and Rob does 12/30 of the job.
12/20 = .6
12/30 = .4
Total = 1 job done.
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