How Long Does it Take For a Ban to Go Through?

The other day I had the displeasure of playing with one of the most toxic people I've met in this game. He was constantly swearing at both teams, and when things didn't go his way, started to intentionally assist the enemy team, posting ":)" in chat while he did it. Despite my entire team reporting the player, I see that they're still playing games and have received no notification they have been punished. It seems like my reports never do anything in this game, and I'm not sure how the League community is going to improve if there is no consequence for their immature behaviour. I understand we all have our bad days/games, but some behaviour is inexcusable. At this point, I don't see the point in reporting anyone.
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