Is this a good way of teaching this lesson?

I do some online tutoring. I was given a problem by a student and I did not do a very good job of explaining it. The problem is not difficult if seen in the right way. The difficulty is in seeing it the right way. Afterward I thought of an approach that I would like to test out here. The basic strategy is this. I am going to present a problem like the original one. Then I am going to present a similar problem that I think is intuitively easier. I will use Socratic method on this second problem and then return to the original.

Original type of problem:
If Joe can paint a room in 6 hours and Sally can paint it in 3 hours, how long does it take for them to paint the room if they do it together?

Now consider this modified version of the problem.
Joe can paint 3 rooms an hour and Sally can paint 2 rooms an hour.

1. When they work together, at what rate can they paint rooms?
2. How long will it take them working together to paint 15 rooms?
3. How long will it take for them working together to paint 1 room?

Back to the original problem.
1. What are the individual rates at which Joe and Sally paint rooms expressed as rooms per hour?
2. What is their combined rate?
3. How long will it take for them to complete one room?