As for the distance it sounds a long way. I do about 19 miles each way, takes about an hour. So thats 2 hours cycling every day. I rarely manage 5 days a week. You'll be doing closer to 3-4 hours each day so building up in 3 weeks is too much, you'll exhaust yourself.
I'm just starting back after some time off the bike due to theft of my bike (and winter). I find that the best thing to do is to try one day a week for a few weeks. Then every second day for a few weeks. The real killer change is two days in a row. So try Mon, Tues, Thurs, Friday for a bit. I'd say you're looking at 6-8 weeks to build up to 5 days.
Don't rush it or you'll injure yourself or end up hating the ride. You'll also find that most of your time outside work is spent eating and sleeping to get ready for the commute. Which is perfect, eating, sleeping and cycling are some of my favourite things.
Good luck with it.
(of course, I may be an unfit wuss and thats why it takes me so long to build up!)