Puzzle!!!!

Hi,
Here is an interesting puzzle. Solve this!!!

A monk stays in a hut on the edge of a forest, next to a small hill. On top of the hill is a temple. There is only one path that leads from the monk’s hut to the temple and it winds through the hill. One day the monk leaves his hut at 9 AM, walking along the path towards the temple, traveling at his own speed, resting at times. He reaches the temple at 9 PM and stays overnight. He starts his journey back at 9 AM on the second day, along the same path, again traveling at random speeds, and reaches his hut twelve hours later, at 9 PM.

You have to prove there is at least one point on the path that the monk crossed at the same numerical value for time on both the journeys (i.e. he crossed a particular point at X am or pm while traveling to the temple and at exactly X am or pm whatever the case may be on the return journey).