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This question comes up quite a bit, especially since the advent of totally unrealistic 'estimates' of driving times that come from computer-based programs that ignore the need to stop for food, fuel, and bathroom breaks, and also assume that you'll be able to drive at or above the speed limit for every minute you're behind the wheel, even through stop lights. Perhaps the best real-world determination of what's safe to drive in a day comes from the limits placed on professional long-haul drivers by the US Department of Transportation. While those limits are given in terms of hours, they translate into roughly 600 miles per day. Yes, one can drive farther than that, say 700 miles, on a given day but not day after day after day. And NEVER a thousand miles in a day if you expect to be able to do anything at all the next day. On a long haul such as the 3,000 mile drive you're contemplating, five days would be the absolute minimum to complete it safely. Six would be better. And please do not come back here and brag that you foolishly tried to do it in three, somehow managed to beat the Russian Roulette odds, and thus encourage others to engage in similar practices that put at risk the lives of every other motorist who has to share the roads with a sleep-deprived 'driver'.
AZBuck