Find the largest and thickest towel available in your hotel room. This towel should be clean (used for showering).
Put a piece of clothing on top of the towel.
Roll up the clothing such that the towel is nicely wrapped with the clothing.
Do so until you have rolled up the entire clothing.
Twist the roll as tightly as you can, throughout the entire length of the clothing. This will drain out extra water in the clothing.
Let your laundry dry in the hotel, it should take less time for them to dry. You can then re-wear your tshirt & travel with less clothes!