Spelling it out in six easy steps

a) Light travels from A to B, distance 80, speed 5, time 16.
b) Light travels from B to A, distance -80, speed -5, time 16.
c) Light travels from A' to B', distance 40, speed 5, time 8.
d) Light travels from B' to A', distance -40, speed -5, time 16.

Ok so far..
Now we map A to A' and B to B'

e) Light travels from A' to B, distance 80, speed 5, time 16.
f) Light travels from B to A', distance -20, speed -5, time 4.

The  distance(AB') =/= distance(B'A) in relativity.
So what does Einstein do?
He takes the average time and the average distance. That is
what the 1/2 is for.
  http://www.androcles01.pwp.blueyonder.co.uk/Rocket/eq22.A.GIF

Androcles