Beijing Capital Airport Terminal 1 to 3

I am a US citizen, and have a connecting flight (international) arriving at 6:20 PM (Thursday) from JFK, and leaving from Terminal 3 at 8:00 PM for Manila. After reading, this is making me nervous, with an hour and 40 minutes. Could someone walk me through the exact procedure and the probably time crunch? My bags will be interlined, and I'm fine taking no carry-on if that will speed things up.