More to the point, I doubt that there is an Amtrak train that speeds at all without it being common knowledge. These things are timed from station to station and the station chief knows how long it takes going 60 mph.
The other issue though, is these things arrive and depart at stations on a timetable . . . very rarely do they deviate from that. If the train is scheduled to arrive at 1:23 a.m., it is going to arrive very much in the vicinity of 1:23 a.m.