they are in a hurry to get a speeding ticket or in a hurry to get to the hospital via a car-wreck. If I speed up, I may get a ticket as well, if I don't get out of the way I may end up in a car-wreck as well.

I just let them pass, usually I'll see them pulled over by a cop further down the road, or find them stopped at a stoplight right next to my car, or find them in a wreck that slows down the rest of the traffic.