This isn't homework, just for fun. I got this from a book years ago. If you have read the book or solved it otherwise in the past, please refrain from blurting out the answer. :-)

A man walks up a path that circles a moutain in a spiral. He starts at 6:00 in the morning and arrives at the top at 3:00 in the afternoon. The next day, he begins his descent at 6:00 in the morning and arrives at the bottom at 3:00 in the afternoon.

The grade of the path is a constant 15 degrees, the altitude at the top is 5000 feet, and the man is 5'10" and weights 160 lbs. He is carrying nothing but a small 32 oz. water bottle that is full at the start of both trips.

Problem: Prove that he was at the exact same spot on the path at the exact same time on both days.