Won't the bees that are left raise a queen and keep going?
Yes. The problem is this: This is PRIME egg laying/brood rearing time. The queen can lay 2000 (!!!!) eggs a day. They need to have lots of workers to raise brood and forage for nectar/pollen for food.
The colony knows it doesn't have a queen. (Called, appropriately, "queenless"). They have to have a less than 3-day old larva to feed royal jelly to make it turn into a queen. They will probably do this. 18 days later, one, but probably more, will hatch as a queen. There can be only one, so hopefully one hatches ahead of any others and kills the rest that hatch. Brutal, huh?
That's approximately 3 weeks from now.
She hangs around the hive for about a week, then goes on her mating flight. Assuming she comes back to the hive -- 20% don't for one reason or another (hit by a car, eaten by a dragonfly, etc.) -- she starts laying eggs. It takes 21 days to hatch the workers.
That's 7 weeks from now, or early August. That is when they should be filling up the hive with honey for the winter. And they will be just starting with new brood. Waaaaaay behind the curve.
Worker bees are female, they can lay eggs. The problem with that is that they are unmated, so they can only make drones, the males. Only a mated queen can lay fertilized eggs.
We aren't sure which hive swarmed. Hubby thinks it's the new hive, and it would be easy to tell when we open it. We bought a "nuc" (nucleus colony) and installed it about 10 days ago. If that hive swarmed, there would be very few bees remaining. The queen was also marked with a blue dot. (Yes, marking a queen is a thing that people who raise and sell nucs do. There's even a color code for the year. This year, all marked queens have blue dots.)
If it's our other hive, it will be hard to tell if they have a queen. (The term for that is "queenright.") That is/was a mature, thriving colony. When we bought that nuc, the queen was not marked, and they may have requeened since we got it. This is its 3rd summer.
We may sound like we know a lot, but really... we're still very inexperienced.