Two new key dates: August 16th and September 16th

Eggs were put into this hive on July 30th. If the hive attends to those eggs, drawing out queen cells, capping them and the hive is successful in maintaining them, a new queen should emerge on Day 16 which us August 14th.
It will take her a couple of days to get oriented then a few more days to take her mating flight.
If the weather cooperates, then it's 24 days or nearly a whole month from the time she emerges until the first bees that she lays emerge.
By the middle of September the newbies should be here. I'm calculating about 45 days from egg (potrntial queen) to new eggs.
I've been feeding them a little bit stronger than a 1:1  solution.
To be honest, I don't want to go into the hive until after the 14th of August. That will be next weekend. It's just as well as this is been a relatively rainy weekend.

First you don't succeed . . .

I waited until July 22th to check and see the progress of this Hive. It was clear that nothing good was going on. I was happy to see that there were no laying workers but there was also no brood and there was the very beginning of a larvae out burst of small hive beetles. The bee population was enough to keep things under control but I needed to do something, and I needed to do it right away.
I beekeeping friends if they might have two frames of brood and eggs to give me, sell me or trade me. My good friend Michelle came through on Monday July 30th with 3 frames.
They contained quite a few eggs as well as brood in all stages and lots of nurse bees. We did a full inspection and removed the bad frames leaving them in the field so that they could be robbed out. I took one frame for freezing to feed back to the bees later and put on sugar water for food to encourage the bees.
Although the bees look small, and the population was reduced  it was sufficient to take care of this brood box until they create a queen.
I will check this again on the weekend to make sure they've started drawing out the egg comb in into queen cells.
If they haven't, and I can't find a mated queen, this hive may be lost. If they have, there may be sufficient time left in the season for the queen they create to be mated and to keep the hive going through fall and winter.
If that's the case, and the queen lays a good pattern, I will keep her, otherwise I'll requeen in the spring.
We also put in beetle blasters with three drops each of the recommended poison so that the small hive beetles don't get out of control. I checked the other day and had already started seeing it work.
Now again it's just a matter of time.