Question

Sam and Cam have a lawn-mowing service. Their first job tomorrow morning is one that usually takes Sam 40 minutes to do alone, or Cam 30 minutes to do alone. This time they are going to team up, Sam starting at one side and Cam at the other side. The problem is to predict how many minutes it will take them to finish the job. What part of the lawn will Sam complete in the first ten minutes? What part of the lawn will Cam completely in the first ten minutes? What part of the lawn will the team complete in ten minutes?

Answer 1

Sam can his 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 long does it take?
.
1/20*x + 1/30*x = 1 job done
, where x = minutes.

Multiply everything by 60 to get rid of the fractions.
3x + 2x = 60
5x = 60
.
Divide both sides by 12
x = 12
.
So the answer for working together it will take them 12 minutes.