Part of the difficulty of this problem is that for parts (b) and (c) I use unfamiliar terminology to pose the question. Part of the challenge in dealing with this problem is to interpret the unfamiliar terms in context and to see what is happening.
Parts (a) and (b) would be good for an exam problem. Part (c) is very attractice conceptually, but the algebra makes it just a little too long to consider using on a short hour exam. However, I might very well use this for a homework problem in the future.