the traviling monk

Prove that there must be a spot along the path that the monk will pass exactly the same time of day? He leaves at 6 am. Stops to drink coffee. stops to smell flowers. stops to take a nap. stops for power bar. stops to talk with a monk. arrives at 6 pm. prays. leaves at 6 am dose the same things going down . coffee,smell flowers,take nap, power bar, talk with monk. arrives at 6 pm at bottom