So 100 Prestige Points cost 2200 tokens. You get 200 from buying the Event Pass, and I would guess you probably get more than 200 for the Missions, but I'll just count with 200, even though it will most likely be a little more. So anyway, that's 1800 tokens to earn through grinding.
If you play every day, you need to earn 59 tokens daily to be able to purchase the Prestige Points at the end of the event. You may not play every day, but you can make up for it playing a ilttle more other days.
First win of the day grants 18 tokens, that's 41 tokens daily excluding first wins.
Summoner's Rift wins give 12 tokens, losses give 6 tokens, ARAM wins give 8 tokens, losses give 4 tokens. Let's assume you have a 50% winrate. With enough games played, that would main you gain roughly 9 tokens for every SR game, and 6 tokens for every ARAM game.
According to statistics, the average length of SR is 28 minutes. Champion select with loading screen is probably around 8 minutes. Queue time is around 1 minute, but I'll count with 2 to make up for the rare dodges, making it 38 minutes to play a Summoner's Rift game on average, with everything included.
Average ARAM length is around 20 minutes. Just queued up for a game and dodged it to check the champion select duration, and it's 65 seconds. With loading screen included it's somewhere around 4 minutes. The queue time isa little lower, but there are a little more dodges, so I'll just calculate it with 2 minutes as well. That's 26 minutes for an ARAM game.
So to get your 41 tokens daily, you need to play 4.55 SR games a day, which takes 173 minutes with queue, champion select, all that, which is almost 3 hours.
If you play ARAM, you need to play on average 6.83 games a day, which takes 191 minutes.
So by playing Summoner's Rift, you get your tokens faster. Riot also made it so that you don't actually need to win to get your first win of the day bonus, if you play 3 games you also get it, so that the frustration when you're on a losing streak isn't that bad.
So to sum it up, if you want the 100 Prestige Points, you have to play 3 hours a day on average, but you can do it like playing 5 hours one day and playing 1 hour the other day when you are busy as long as you get the first win of the day. If you miss a first win of the day, you need to play 2 SR or 3 ARAM to make up for it.
Well, I hope that helped, best of luck to everyone!