Problem Solving

I came across an interesting problem in Zeitz's book. It's stumped me, any help?
Two towns, A and B, are connected by a road. At sunrise, Pat begins biking
from A to B along this road, while simultaneously Dan begins biking from B to
A. Each person bikes at a constant speed, and they cross paths at noon. Pat
reaches B at 6pm while Dana reaches A at 9pm. When was sunrise?

let 's call C the place they crossed at noon so 12:00, C to B takes 6 hours as pat arrives at 6, C to A takes 9 hours as dan arrives at 9
6+9= 15 so as pat reaches B at 6 pm
pat  left at 6 PM - 15 hours it gives me 1 AM...