Okay. Let's assume that they both walk at the same rate and they both ride at the same rate. Let's also assume that they ride three times faster than they walk (makes my example easier, and it shouldn't make much difference). Assume that there are a number of equidistant points labelled O (for Origin), A, B, C, D, etc.

For our origin, let's assume that the first ``leg'' has already been undertaken. That is, traveller 1 has already ridden the bike ahead, and let's assume that he got to point A while traveller 2 is back at the Origin. Their pattern looks like this:

        *               *               *

O 1 A 3 D 1 E 1 F 1 G 3 J 1 K 1 L 1 M 3 P 1 Q ...

A 1 B 1 C 1 D 3 G 1 H 1 I 1 J 3 M 1 N 1 O 1 P ...

*               *               *

The letters are the ``milestones'' and the numbers are the distances they travelled. The asterisks are where they left the bike. If they were to walk, then this would be the pattern:

O 1 A 1 B 1 C 1 D 1 E 1 F 1 G 1 H 1 I 1 J 1 K ...

You can see that they're already way behind in the same amount of time. I can't think of a reason for the pattern to not continue (<- split infinitive ).

Edit: Try to make it a little more legible.

Also, we're not taking into account all the hoodlums that will be stealing the bike's wheel.