Any suggestions besides the normal do bounties, do missions, etc.
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Make a character early in the day, do all your missions on heroic, and any bounties you receive while leveling. Then when you hit 16+ do any and all bounties you like. Whether or not you're 20 already by the time of the reset, do those new bounties and you'll be a 20 easy. Or if you can do it fast enough do it later in the day. Either way it should take more than 10 hours.