$20 an hour is extremely reasonable in all the places I have lived. That is what I charged in high school (10-15 years ago).
I charge $30 an hour for music lessons right now (and then give people a discount for watching my kids during the lesson, so it still works out to $10 for a half hour lesson) and I feel like I’m “undercharging” and that’s OK at this time in my life (then I don’t feel bad cancelling if my kids get sick or if I want to take a 2-3 month maternity leave).
However, for that price I would expect a good amount of professionalism from the high school student. Like regularly scheduled lessons (not just on and off whenever it works out), that the teacher write out a list of practice suggestions/notes for the week. I would expect that for that price, the teacher has had a good amount of lessons themselves and at least some experience teaching lessons.
We are blessed to be in an area where rates are lower – about $10 for half hour lesson on violin, piano, guitar. But when we lived in Texas $25 a half hour was standard. Maybe look at craigslist or online in your area to see what the going rate is. I wouldn’t offer a high school student the full rate – he is learning to teach on your child. I would offer about 30% less than the standard rate a professional charges.
Definitely….also ask about bartering. Can you clean while the kids have their lesson? Or bring baked goods? Or a meal? Perhaps the kids can have a lesson every other week – that’s not always recommended, but depepnding on the student and how they practice, I have done it.