Random Ping Spikes

Hi, I don't know if this is the right board to be posting in, but it is definitely something that is affecting my gameplay experience...

I play on the NA servers, and I've been struggling a lot right now with a lot of random ping spikes, and I don't exactly understand why. My ping usually stays from 20-30 ms, but recently it's been spiking every few minutes in games for 30 seconds at a time to 400+. I've tried everything I could think of to fix this problem, but I'm kind of stuck now.

As you can see here, my internet speeds are very fast and are definitely more than sufficient to play LoL. http://www.speedtest.net/result/7008689112.png

I ran a prolonged ping in command prompt with "ping 104.160.131.3 -t", and this is what I got after a little bit: https://i.imgur.com/AzxPWan.png

If anyone has a solution or has experienced similar problems to this, please let me know. I just wanna play LoL without getting flamed for getting killed when my ping spikes...