how fast are 13 inch trailer tires going when my truck is going 55mph with 15" tires

55 mph= 55mph*5280 ft/mi * 12 in/ft /(60 min/h)

= 58080 in/min
Each revolution of the trailer tire travels a distance equal to the circumference of the tire
=(13)*π inches
Number of revolutions per minute
=58080/13π
=1422 rpm approx.

Note: the answer is the same if the car uses 16" tires. It's the speed of the trailer that counts.