It's hard to say, every tank is different, but generally it's anywhere from 2-5 weeks maybe? I did a fishless cycle so I can't really speak to fish-in cycles, but on average probably a few weeks.
If you can't do a
pwc in the morning I'd do two large ones tonight as I mentioned earlier to get the nitrite as close to 0 as possible. Hopefully it won't spike too much by the time you come home tomorrow night. You'll start to get a feel for how fast they are rising so at some point you may need to get up earlier just to do a
pwc before work and then another after.
Ammonia should start dropping to 0 (but keep testing for it anyway) and nitrites will rise as you've already seen. Don't let them get too high; again under .25 is ideal for the fish as nitrites are toxic to them. The nitrite phase is tricky b/c they'll want to spike fairly quickly so as I said you may need to shift your schedule around a bit to get an extra
pwc in there in the morning but I could be wrong, just let the tests tell you when to do a water change (or more than one, as in the case tonight). Nitrates will start to rise too but with all the
pwc you'll be doing to keep nitrites down the nitrates won't get close to harmful levels.
Then after a while nitrites will come down and stay at 0 on their own. Then you'll just do your weekly maintenance water change (about 50% once per week is a good routine).
Also what dechlorinator are you using? If you can get some Prime, it will help detoxify the ammonia and nitrite in the tank until you can do a water change (but not to be used in place of water changes; water changes are very important now and will help save your fish through the process. But you seem to have a good understanding of this so far.

).
Good luck.