1 week as a builder, 1 week as a resident, 4 weeks as a mayor, and now I am a President. Not sure how long it will take to tycoon though.
Keep in mind, I play more than I should. I play probably 5-10 hours a day and thats conservative. I started ECC in mid december and am now a President/Moderator. It took me a week or so to get res. A month to get mayor and a a few weeks to get President.
I started off mining redstone, and spent about 2 days mining. Then I took up a job farming pumpkins (I believe they were $2.50 each at that time) and made the rest of the money for resident in a day. Then a friend and I split the cost to get me mayor. Though had we not split the cost, and at the rate I was earning money, I probably could have gotten mayor by myself in about 7-8 days. I had spent 15k as a resident for a 30x30 plot as well, so had I not done that I probably could have gotten mayor sooner. I kept harvesting pumpkins up until I bought my portal and then switched to the exp market (which at the time was 36k for 50 lvls, and lowered to about 18k a few weeks later). I have also never won the lotto, so I've earned pretty much everything I've bought so far.