Train A leaves the station at 1:45 traveling at a constant speed of 65 mph. If it arrives at its destination at 3:15, how many miles did it travel?
The time it takes for Train A to travel from 1:45 to 3:15 is 3 hours and 15 minutes - 1 hour and 45 minutes = 1 hour and 30 minutes.
Since Train A is traveling at a constant speed of 65 mph, the distance it travels in 1 hour and 30 minutes is 65 miles/hour * 1.5 hours = <<65*1.5=97.5>>97.5 miles. Answer: \boxed{97.5}.