It depends on who you take them with. I believe private lessons are most valuable to people who are at the purple belt level or higher. They can seriously jump your game up BIG time if you train with the right guys. I learned some tiny details on many movements and positions I would routinely use every time I sparred, and this just changed everything.
I'm sure if you mention where you live, people can recommend some good guys for private lessons. I've never had a problem with people looking at the clock. Usually they go over a few minutes, sometimes more.
Another thing, it isn't a good idea to go to a private with nothing in mind. You should prepare before hand and write down things that are giving you problems so you know what to ask. That will save you a ton of time with your private lesson so you don't end up seeing stuff you don't want to learn or already know.
A really good teacher will be able to roll with you and pinpoint a bunch of things you need to work on and then focus the private lesson on those things. However, I can't even guess the percentage of teachers who would be able to use that approach and leave you satisfied with your money spent.