It takes gary 1 hour to milk all the cows, and it takes dana 1.5 hours. how long will it take them to do the job together? explain all the steps and models/equations used. so much.

It takes Gary 1 hour to milk all the cows.  1 hour per job ==> 1 job per hour.

It takes Dana 1.5 hours.  1.5 hour per job ==> 1/1.5 job per hour.

Working together, they can do (1/1 + 1/1.5) job per hour.

To add these fractions, put them over a common denominator:

(1/1 + 1/1.5) = (1.5/1.5 + 1/1.5) = (2.5/1.5) = 5/3 job per hour.

5/3 job per hour ==> 3/5 hour per job.

3/5 hour = 36 minutes.

That they are numbers and related to each other.