OM and OP will coincide a second time after 120 seconds. You could visualize it as ray OP moving at 3 degrees/second relative to OM. Using this visualization, we find that OM makes 30*60*3/360 rotations (minutes * 60 * rotational speed/360 degrees in a rotation), which is 15, and that OP makes 30*60*6/360 or 30 rotations, which is 15 more than OM.
