Sorry bobbinwales, only just noticed your question. Presumably they are walking along the beach together, so wherever 'there' is, they will get there together, neither will be first.
Or mabe the beach was infintely long so they never got there, or maybe the answers neither cos they were walking in the wrong direction.
The riddle isnt a proper riddle IMO... theres something missing surely
It might be a bit obscure, that is what riddles are, a straightforward question is hardly a riddle. As the riddle is posed I think neither is probably the best answer.