Anyway, a good rule of thumb is an average is 55-60 miles per RIDING day. Obviously, some only do 25 miles per day and other super-strong riders do 125 miles on average (and miss a lot). Figure roughly 2,800 miles or about 51 days on the second option I showed. The ACA routes page will break down the various routes and segments to be more exact.
If you are trying to do it during the summer break, I would definitely do east to west as the western mountains may still have cooler weather and/or a few mountain passes MAY still be closed with snow. Plus you will be stronger for the longer climbs once you get there and then you can do any route you want. If home-schooled, west to east is slightly better due to a slight tailwind favoring. Regardless, I did my first TransAm route when I was 14. I missed the first week of school and can tell you the experience was a LOT better than the first week of school.