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If you are driving on Interstates just to get from point A to point B, 600 miles is as far as you would want to go in one day, in fact this is what professional drivers are limited to by law. With normal brief stops for food, fuel, and bathroom this will be about a 12 hour day. On non-Interstates and/or with sightseeing stops this of course will be less. If you have 3 weeks to do a 3000 mile trip I doubt that you will have a problem. However, it's very normal for people to THINK it's going to take less time to do something than it actually does, especially younger people.

12 hours will also eat up all your daylight, why drive at night when you can't see anything?