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?

When was sunrise?
In the morning.

4:39 am
Here's an example situation:
The distance is 1+(sqrt(6)/2) mi
Dana is traveling at sqrt(6)/18 mi/hr
Pat at 1/6 mi/hr
Really slow, I guess.
By noon, Dana has traveled 1 mile and Pat has traveled sqrt(6)/2 miles.  It takes Dana 9 hours to cover the remaining sqrt(6)/2 hours and it takes Pat 6 hours to cover the remaining 1 mile.

I just messed around with the ratio between Pat and Dana's speed until I got the right answer.

>>1

Here's my solution:

P(12-x)=D(21-12)=9D
D(12-x)=P(18-12)=6P

it's easy to work it out if you start like this.
* x is sunrise time
* P is speed of Pat, D is speed of D
* The two equations basically say that what distance pat travelled before noon is the same what Dana traveled after, and vice versa.

and yes, the answer is 4:39

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...

>>5

they ride with the same speed, traveling the same distance and yet it takes different amount of time
6pm - 15 is 1

they don't drive at the same speed, each one has a constant one but their own

the problem seems to be a little bit too fanciful
if the sunrise was at the same time in the 2 towns and then the noon was at the same time and then the time of their arrivals was in the same time zones (travelling whole fucking day) then it should have been very unique event of positioning of sun and earth and the towns and the road.

Maybe it's the same road but it runs in and out through both towns in a figure eight shape, with both sides having a common intersection, and going one way is the "long way" while the other is the "short way."

Fact:
Dana =\= Dan.
Problem solved, bring in the dancing lobsters.

>>8
Or maybe the road goes from north to south.