Rendezvous at Noon

[From the Fourth Annual Iowa Collegiate Mathematics Competition. Written by Paul Zeitz. Slight modifications by Sam Rebelsky.]

Grinnell and Newton are connected by route six. At sunrise, Pat begins biking from Grinnell to Newton along this road while simultaneously Dana begins running from Newton to Grinnell. Each person moves at a constant speed. They cross paths at noon. Pat reaches Newton at 5pm while Dana reaches Grinnell at 11:15pm. When was sunrise?

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