Question

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?

Answer 1

`(1)/(3)+(1)/(4)=(1)/(x)\\ (4)/(12)+(3)/(12)=(1)/(x)\\ (7)/(12)=(1)/(x)\\ 7x=12\\ x=(12)/(7)\hbox { h}=1\hbox{ h }42\hbox{ min } 51.43 \hbox{ s}`

Answer 2

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