3-6 minutes a game, and of the remakes I've seen 100% have been at 3 minutes. So I'd venture a guess that it's at least 2/3 at 3 minutes so maybe 4 minute average, plus queue time and champ select so maybe 5-6 minutes a game.
Yea, that would be about 20 minutes. Maybe doing an IP reward for consecutive remakes would be a fair solution. Maybe getting some IP reward for each remake after 2 in a row (in a short time period absolutely no games or logging out in between).
It really would be a small fix and would only handle cases like this where someone has multiple remakes in a row. That's not something anybody could really try to plan and avoid in matchmaking.