Light speed question

I remember my friend told me about a light speed contradiction. It went as follows:

If there is a train circling the earth going just less than the speed of light (ignoring some physics) and you were on the train, you would be traveling just less than the speed of light. If you were to walk or run toward the front of the train, you could go faster than the speed of light.

Is this theoretically reasonable, or is there something that makes it not work, other than the Centrifugal force of going around the earth at such speed? I am just wondering...

That's a great thought experiment, but as it turns out, the "walker" still won't exceed lightspeed. The reason is that speeds don't "add" in the normal way when things are moving really fast. If the walker on the train is measuring his own pace as (say) 3 miles per hour, then somebody on the outside would measure the walker's pace (relative to the train) as something LESS than 3 mph. This fact manifests itself as "time dilation", which means the outside observer sees all the people on board the train as though they were moving about in slow motion (for example, it might take 10 seconds for the walker to take a single step). And the closer the train gets to lightspeed, the more time slows down aboard the train. The result is that the walker can't ever exceed lightspeed from anybody's point of view.

You wouldn't be able to walk toward the front of the train. That is what makes it impossible. It's because at that velocity your mass would be too great to do so.

And Einstein's theory simply implies anything which has a velocity less than that of light is not able to obtain a velocity which is that of light of greater. It doesn't state that something cannot already have a velocity greater than that of light and maintain that velocity. That is where that other person gets it wrong.