The idea that IP is based on time is only partially correct. Here's a sample of my latest matches from Normal(Blind Pick):
N | Victory | Time | Time (seconds) | IP | Seconds/IP | K/D/A | Gold | CS | Level
- Victory, 29:06, 1766 Secs, 85 IP, ~20.78 secs/IP, 5/5/8, 9k Gold, 48 CS, Level 14
- Defeat, 35:11, 2111 secs , 65IP, ~32.48 secs/IP, 3/9/4, 10k Gold, 89 CS, Level 14
- Victory, 37:05, 2225 secs , 103IP, ~21.60 secs/IP, 7/3/11, 13k Gold, 93 CS, Level 17
- Victory, 39:04, 2344 secs , 108IP, ~21.70 secs/IP, 3/6/9, 11k Gold, 84 CS, Level 15
- Defeat, 29:20, 1760 secs , 57IP, ~30.88 secs/IP, 0/10/8, 7k Gold, 62 CS, Level 13
The same champion was used for each match, the matches are in chronological order with the latest match first. First win of the day had been expended in a previous match.
Take note of the "Seconds/IP" 'column', it seems that IP is based on performance as well as time. However, my Seconds/IP value was better for game 1 than game 3, even though my strictly numerical performance was worse. The difference is that I bough a sighstone and upgraded the yellow trinket to ward aggressively for the team.
It seems that there is one clear trend: if you win you get more IP. Warding seems to also play a part, but that's really just a guess. it might also be something like team composition or team performance over-all that affect IP. So here are our team stats:
N | Gold | K/D/A | Composition
1 49k 43/22/32 TF, LB, Ash, Garen, Wu
2 42k 19/35/17 LB, Ash, Jax, Li, TF
3 57k 35/42/38 Voli, Xin, TF, Aat, Li
4 49k 26/43/24 Jinx, Kat, Var, Ash, Twitch
5 35k 19/45/20 Aat, Li, Tryn, TF, Vay
Notice that our overall K/D is better in game 1 than game 3 & game 4, however our A/K is worse. If it was as simple as K/D I'd expect to see a bigger discrepancy in Seconds/IP: game has ~2.0 K/D, while 3 has roughly ~0.8 and game 4 roughly ~0.6 .
But this is just speculation, although it seems clear that there is a performance factor in how much IP you get. This limited sampling of matches also seem to support the idea there is diminishing returns.