Question

Steve can mow the lawn in 30 minutes by himself. Cathy can mow the same lawn in 50 minutes by herself. How long will it take to mow the lawn if they work together?​

Answer 1

1 job done

Explanation:

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.