If these were things were happening simultaneous in time you’d be a hundred percent correct. But that isn’t the way the question was posed.

It’s inarguable if you change their relative speeds on 100 different passes of the problem they would always meet at a different point on the path if they’re doing it at the same time- that very variability shows that if you displace the relative journeys in time there is no necessary shared intercept point in time/space sunrise to sunset.