Nearly everyone that's flown United from LA to Hawaii has played this.  They give you some information like airspeed for the first half of the flight, total distance, takeoff time, wind correction factor but I contend it'a still mostly a guess.

I had a GPS with me and got a location near the time I originally figured.  Some quick re-figuring told me this guess was wrong by about 10 minutes, so a few minutes before what my GPS was telling me would be halfway I started to watch the miles tick off and when it hit 1314 miles (regular miles, not nautical miles) I checked the time and wrote it down.  I got second place, someone nearby (maybe they overheard my prediction:() was about 10 seconds closer.

I contend you'd have to have some pretty good information on takeoff of the climb rate, time to cruise speed, etc to really even make a good guess, let alone the change in the tail or head wind.  I checked on the way back and we went 500 miles in the first hour after takeoff and 588 miles in the second hour.  Both directions we landed early, 30 minutes on the way back.

I participated in a machine gun shoot halfway to Hawaii.  Nice place.