I'm driving at 50. Your doing 100, but start 1 mile behind me. After x amount of time, your halfway to where I started (i.e gone 0.5 miles), but i've moved a bit (.25 miles). You move half the distance between us again after x amount of time, but again I move a little bit more. repeat ad infinitum.
Why do I only travel half the distance between us? I'm doing 100 in my XRT and you're doing 50 in your UF1. Eventually I will have to overtake you because I'm going at double the speed. If this isn't true I should probably start drinking.
EDIT - I understand where the logic comes from, it's just the laws of physics that always seem to ruin these crazy puzzles. I guess it means we'll have to re-think mathematics though...
Because while evntually you will overtake me, if you think of it in terms of "you half the distance between us" it will go on forever, with the length of timing getting smaller and smaller to inifinity
That would be the case if MP3 stopped after 0.5 miles and allowed you to do your 0.25 miles at a seperate time, but because you're both moving at the same time, MP3 can cover 0.5 miles during the period of time in which you have covered only 0.25 miles, thus allowing him to gain on you.
The problem or solution is that you're continuing to look at a smaller and smaller time frame and are basically slowing down and stopping time right before/as he passes. There's really nothing special about it, other than that it easily confuses you the first time you think about it.