Okay, suppose we have two people, one being 50 kg and the other being 100 kg; they are separated by 600 m, with each person holding on the end of a rope of negligible mass. Why is it, that when one of the two people creates a tension in the string, they meet at their center of mass? Also, how my friend solved a problem similar to this one, was that he said since the one person is half as heavy, that person will travel twice as far; so, 2x + x = 600 m. Why do both of these methods work? Could someone fill in the reasoning behind each method, please? I'd like to understand why both work.