Suppose that a person with a push mower can mow a large lawn in 2 hours, whereas the lawn can be mowed with a riding lawn mower in 1 hours. working together, how long will it take to mow the lawn

Working together, the job takes x hours to do.

If a lawn can be mowed with a push mower is 2 hours, then in 1 hour, you do 1/2 of the job.

If the same lawn can be mowed with a riding mower in 1 hour, then in 1 hour you do 1 job.

If the same lawn can be mowed by the two mowers together in x hours, then in 1 hour you get 1/x done.

1/2 + 1 = 1/x

3/2 = 1/x

x = 2/3

They take 2/3 of an hour. 2/3 * 60 min = 40 minutes.