This concept may have been discussed before, but I couldn't really find any that asked the same question. Through multiple sources, I have discovered that, in the LHC, we have the ability to propel protons to 99.99999% the speed of light (relative to a stationary object), and make them collide. But, what if we make them pass each other? Wouldn't one proton be traveling at 199.99998% the speed of light relative to the other? I asked one of my teachers about this and she said that it doesn't work that way, but couldn't explain why. Isn't that the definition of relativity? I'm a high school student working on a senior project (not as homework), so don't be afraid to simplify it (I actually encourage that).