How to earn IP fast?

ARAM. Faster games that remove a lot of the player related non-sense that can slow down a marathon of point farming.

Plus if someone skin boosts ya get more. :D

Yes, faster games yield a better IP/time ratio. Although there's also the time involved in matchmaking to consider, so queues with fast matchmaking offer some advantage.

I actually find i earn the most IP in co-op, simply because i have to take fewer breaks. ARAM (at least the way i play it) is stressful. I'm trying hard and typing to my team to teach them how to play the game (or at least the way i think it should be played) at the same time i'm trying to dodge skillshots. Co-op is not stressful at all so i can keep zombie playing for hours on end without interruption. ARAM is more fun though so that's usually what i do.