A Short Parable About a Monk

Say exactly at sunrise, a young Tibetian monk begins to climb up a mountain to meditate at the temple for a few days.

He goes along a narrow and treacherous path. Of course, along the way, he gets very hungry, and he has to stop to eat. Perhaps sometimes he stops to take a whiz off the edge of the trail. (Hey, he is only human. He will publicly urinate if he has to!) He sees some pretty flowers and picks them to decorate the temple with. Obviously his speed of travel varies rather randomly, but eventually he gets to the temple just before sunset. (Lucky for him, because travelling along a treacherous path up a mountain without a flashlight really sucks.)

Once he is at the temple, he spends a few days praying and doing his monk-y things.

A few days later, at sunrise, he stretches, grabs his dried berries, and heads down the path again. Of course, he stops whenever he is hungry or has to pee, and of course, his average speed of descent is faster than his average speed of ascent. So he gets down to the base of the mountain (his house) before sunset.

True or False? There is a point on the trail that the monk was at on both trips at exactly the same time of the day.