Bike Rack (AR Modeling Challenge)

Using only 2 surface equations, how can we reconstruct the arches of this bike rack? Modeling Clues: 1) The radius of the small circle formed by the cross section of the plane x = 0 and this entire surface is 1. 2) The shortest distance from the origin (0,0,0) to the pink surface = 3 units. 3) The greatest distance from the origin (0,0,0) to the blue surface = 5 units. Additional Challenge: View 0:25 - 0:40 in the silent screencast below. How can we "flip" this surface upside down to model the bottom arch of this bike rack?

Quick Demo