So based on 'The speed of your game should never depend on how fast your computer is' I could just slow everything down and it would be the same on every pc? In that case I could just let it 'sleep' every
other second to solve this.
Well, that would slow it down, on average. Between the sleeping periods, it will still run just as fast, and it would be unplayable.
What you want is to make the simulation slower, while continue rendering with as high FPS as your monitor can handle.
You probably don't want to call sleep(), since you can't be sure your game will "wake up" in time for the next frame, and you'll get strutting animation. If you use v-syncing, the driver should block while waiting for the next frame anyway, so you won't burn CPU cycles and battery life for nothing.