I would guess that it would only take 10-15 minutes per day in each of the subjects that he doesn't love to make sure he keeps up and makes decent progress compared to a PS (my DS is in PS and I am amazed how little they actually learn each day).

This seems to me one of the beautiful things about HS, you can dedicate substantial time to the things your child loves, and still make sure they get enough of the other things - without it being so much they get frustrated or unhappy.

Cat