This is a brief breakdown of how long it will take for you to reach Revered.
It takes 21,000 reputation to go from 0 Neutral to 0 Revered. For non-humans, you will get 4050 reputation from the new campaign in Zereth Mortis by the time you finish chapter 7 and unlock your 2nd legendary. If you do each of your 3 weeklies available each week, you’ll gain an additional 7000 reputation by the Tuesday of Week 5. That knocks out 11050 reputation just from weeklies and campaign quests, leaving 9950 reputation to gain from other sources.
World quests give 125 reputation and there are 3 available daily. That means that, barring no other reputation source, you will hit revered 27 days after the patch launches - a full week ahead of when you’ll need to be Revered for your 2nd legendary. You can miss 8 days of world quests and, even if you kill zero rares, you’ll still hit Revered on time. If you miss more than 8 days, there are ways to catch up. Rares give 10-15 reputation per day and there are about 20 of them you can kill each day. Finally, there is a small chance at a +75 reputation token from both World Quests and Daily quests.
TLDR: So, what does this mean for you? It means that as long as you do your three weekly quests and can spend 15-20 minutes a day, 5 days a week, doing 3 world quests, you will easily hit revered by the time you unlock your 2nd legendary. If you miss days, kill rares to catch up.