Test of Reciprocal Time Dilation?

EDIT: confusing 3rd reference frame removed.

I'm guessing the answer to this lies in the relativistic transformation of velocities, but I'm having trouble seeing exactly how.

Essentially, it is the light clock thought experiment but, instead of one observer on the platform, both are on trains moving relative to each other, and relative to the tracks.


The set-up is such that there are two points on the tracks, A and B, which are equidistant from a mid-point M (as below):

========A==========M==========B=========

Alice is moving from left to right (A>B) and Bob in the opposite direction (B>A). Alic and Bob pass each other at point M and zero their clocks.

Is it possible for Alice to measure Bob's velocity relative to the tracks using her instruments?

Even if not, Alice measures her own velocity relative to the tracks (that Bob is running on) - getting a value of 0.4c - she measures the relative velocity between herself and Bob as 0.8c. It would seem that a measurement or calculation of 0.4c (for the relative velocity between Bob and the tracks) is a logical necessity in Alice's frame of reference.

Will Bob make similar meaurements/calculations for Alice's velocity relative to the tracks?

NOTE: there is no switching of reference frames here. Neither Alice nor Bob are trying to ascertain the measurements/co-ordinates of the others reference frame. Each simply makes measurements, using their own instruments, in their own inertial frame.