Simple Rotation + Angular Velocity Question

[AiLove]

This problem is from Tipler's Physics for Scientists and Engineers, Chapter 9, Problem 15.
The tape in a standard VHS videotape cassette has a length L = 246 m; the tape plays for 2.0 h (Figure 9-36). As the tape starts, the full reel has an outer radius of about R = 45 mm, and an inner radius of about r = 12 mm. At some point during the play, both reels have the same angular speed. Calculate this angular speed in rad/s and rev/min.

I've thought about this problem for a while, and I don't understand what they're asking. I assumed the cassette was going at constant angular velocity, but I guess not. I looked at the answer for this problem, the first part of which is below, and it confused me even more. They seem to take some sort of average radius, and then use that as the radius for a w = vr equation. There is a diagram included, which just shows a VHS tape with the radii (12 mm and 45 mm) labeled.

1. At the instant both reels have the same area, 2(Rf^2 - r^2) = R^2 - r^2
2. Solve for Rf
Rf = 32.9 mm = 3.29 cm

Where is the [2(Rf^2 - r^2) = R^2 - r^2] equation from?

 

[Tide]

Those equations simply measure how much tape is on each reel. The left side indicates the two reels contain the same amount of tape (factor of 2) and equating that to the right side says that "tape is conserved." :)