Jack mows the lawn in 3 hours. jane mows the same yard in 4 hours. if they worked together how much time would it take them to mow the yard?

Jack mows 1/3 of the lawn each hour.
Jane mows 1/4 of the lawn each hour.

Working together, they mow (1/3 + 1/4) of the lawn each hour.

In order to add the fractions, you need a common denominator.
12 will work:

(1/3 lawn/hour + 1/4 lawn/hour) = (4/12 + 3/12) = 7/12 lawn/hour.

This rate of work produces 12/7 hour/lawn.

12/7 hour = 1 hour    42 minutes    51.4 seconds