Amtrak is a passenger railroad service that provides medium and long-distance inter-city rail service in the United States. If you have made a plan for a trip and want to book Amtrak tickets on the cheapest fare, then you can book the ticket for Friday & Saturday as Amtrak provides a special discount on these days of the week. If you want to know more information about the cheapest day of the week to travel on Amtrak, then you can follow this link.