Once again semantics.

Expressing the problem as relative rates of the two animals' velocities is misleading, as real animals don't behave like that. While the average relative speeds of the two may be in that ratio at the start, one is not checking on the other to see how fast or far it is 'allowed' to run! A more reasonable 'assumption' is that the relative speeds of the two animals would stay the same, so that one would have to pas the other in newtonian mechanics.

Of course if you have entered the field of quantum mechanics, things are not as 'intuitive' as that, and this problem may very well be a real problem in that field. You then would not be using the normal intellectual tools that you are used to using to solve this problem then as they are meaningless in this field.