Sounds like the perfect opportunity to teach those kids to be a little more patient. Also, when target shooting at the range it's always best to have a second firearm with you to shoot while the other is cooling off. A 22LR is perfect for this and will keep the kiddo's from getting bored. The other thing you can do is make a game of their shooting at the range forcing them to wait so long between shots or shooting the next shot on a different target that requires them to shift their position/aim.
As for how many rounds you can squeeze of fin an hour, that is going to depend on the ammo. Some factory ammo is hotter than others, some powders burn hotter than others, etc. Best to just teach your kids to do the touch test and teach them to stop shooting and let it cool when the barrel gets to hot.
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