To Cross The Cyclist...

What was the scenario?

 Let's suppose he reaches the crossing at 9:00 AM. Usually at 8:30 AM he is at point A, 6 miles before the usual crossing point B (speed of 12 mph, means 6 mile per half hour).

On the day on which he was late by 25 minutes, he must be again at point A (i.e. 6 miles ahead of usual crossing point B) at 8:55 AM. So at this point, both train and man were at the same point A. And the train as everyday, reaches point B at 9:00 AM. That means, it travels 6 miles in 5 minutes. Hence, train must be traveling at 72 mph.