Physics IV.11: Aristotle’s Definition of Time Seems to Fit Distance and Degree of Change; Can It Be Rescued From This Objection?

Physics IV.11: How does Aristotle arrive at his definition of time as the number of motion in respect of before and after?

Aristotle's famous definition of time in his Physics, Book IV, Part 11, is surrounded by quite a bit of motivating and explanatory work. Explain. You need not evaluate this (that's covered by the next question). Please add your answers below. I will add my own in a day or two.