You told me: Speed of A relative to treadmill = 2 feet/sec. Speed of B relative to treadmill = 10 feet/sec. The speeds of A and B were both measured in the treadmill frame, there, were they not? Why are you saying I'm mixing frames? I just used the treadmill frame - the one you told me about. You told me the objects were both moving relative to the treadmill. Is that correct, or not? If not, what were the 2 feet/s and 10 feet/s figures you provided? Also, how could the distance between A and B change if neither of them "have a speed"? If you mean to say they are both stationary, with speed zero, then they'll stay the same distance apart at all times, won't they? That's what the information you gave me about their speeds relative to the treadmill logically implies! 10 feet/s minus 8 feet/s = 2 feet/s. What's the problem? If I stand still on the ground and you run away from me at 2 feet/s, then your speed relative to me is 2 feet/s. I see you moving away from me, and the distance between us increases at 2 feet/s. My speed relative to you as you run away from me is also 2 feet/s. You see me moving away from you, and the distance between us increases at 2 feet/s. Is there a problem? All speeds are relative to something. I may be standing still on the ground, but that doesn't say anything absolute about my speed. It just says my speed is zero relative to the ground. Relative to the Sun, I'm travelling at 30 kilometers per second as I stand still on the ground. If you're operating with some crazy notion that you can identify some object in the universe that is absolutely at rest, then why aren't you measuring all speeds relative to that object, rather than talking about the speeds of A and B along a treadmill, and confusing yourself about which one "actually" has the speed? Everybody can agree that the car's speed relative to the radar gun was 150 MPH. If you want to know the car's speed relative to the Sun instead, the answer is about 30 kilometres per second, plus or minus up to 150 MPH. Is there some kind of problem you're having?