Solving a 20-Year Puzzle: A Sports Car Enthusiast's Homework

[undrcvrbro]

Homework Statement

A dedicated sports car enthusiast polishes the inside and outside surfaces of a hubcap that is a section of a sphere. When he looks into one side of the hubcap, he sees an image of his face 34.0 cm in back of the hubcap. He then turns the hubcap over, keeping it the same distance from his face. He now sees an image of his face 9.4 cm in back of the hubcap.

How far is his face from the hubcap?

Homework Equations

(1/f) = (1/p)+(1/q)
m= -q/p

The Attempt at a Solution

Well, I recognize that there is some sort of theoretical way of solving this, but really...im drawing a blank. My AP physics teacher is a little goofy, and when someone asked him for help on the same problem today we(his students) realized that the answer to the problem he had written down for 20 years was incorrect. Please, anyone...I need your help.

 

[Shooting Star]

If one is a convex mirror, the other side is concave. Given the data, can we tell which image is for which type? The dist of the source is the same in both cases. Is there anything else common for both?