As a non-mathematician / non-physicist (former English major who likes math), I don't have a different formulation, let alone an answer or solution, but a question out of ignorance: Is the time of the race considered to be limitless (infinite)? And an even more ignorant question: if the duration of the race is unlimited, since the speeds of the runners are unknown variables, can one prove that each of the runners will NOT ever be lonely? I realize that if that's the case, then not being able to prove that each of the runners will not ever be lonely isn't the same as proving that each of the runners will at some point be lonely. Just asking.