Two trains leave a station, one going westbound and one going eastbound, both on the same track. A passenger who just wanted to get out of town missed both trains and, while standing on the platform at the edge of the track, observes the westbound train to be receding at 0.6c and the eastbound train to be going 0.8c. There is a very efficient ticket taker on the westbound train going from the back to the front of her train at 0.4c (this is relative to seated passengers on her train, of course)! For both the Galilean and Relativistic velocity transformation equations what would be the speed of the eastbound train with respect to the westbound train (call it ur) according to the observer at the station?
u'=(v-u)/(1- vu/c^2 )
u' is the speed of the train relative to the station observer
v is the speed of the observer relative to the westbound train
u is the speed of the speed of the eastbound train relative to the westbound train
The Attempt at a Solution
I am asking for a "second opinion" I guess you could say. The value that I calculated is 0.5c. I am still trying to wrap my head around these concepts and I am uncertain that if one approaches the speed of light, does the speed of that person (or train in this case) will decrease.
As a side note, I have a strong belief that velocity does decrease due to the fact that time dilates or increases as one approaches the speed of light. If this is true, then the velocity should decrease.
Thanks for your input