If you are on a train going at 50mph, and you pass a train going 50mph in the other direction, how fast are you going relative to that other train? (I think its 100mph but my friends disagree)

It's 100 mph , relative speed = total speed of the two trains .

Its 100mph. If you are in one train, and you look at the ground, It is moving at 50mph relative to you, and the other train is moving at 50mph faster than the ground, so it is going at 50+50 or 100mph.

Let's go with 100 mph.

Here's a good article:

mathforum.org/dr.math/faq/faq.two.trains.html

In a Newtonian world it is 100mph.