One morning you leave base camp at 8:00 a.m. and hike to the top of a mountain where you will spend the night. You arrive at 6:00 p.m. and have a nice dinner at the lodge. The next morning after a truly incredible breakfast you head back down at 8:00 a.m. and arrive back at base camp at 6:00 p.m. Your pace each day varied from hour to hour (minute to minute really) and it might have been very different the second day compared to the first. MUST it be the case that there was a time on day two when you were at the same spot on the hike as you were at that same time on day one?
[This problem sounds goofy but it illustrates an important idea from calculus!] Enter any number you wish in the box below but if you want to attempt this problem and get feedback on it then write up your answer and hand it in to me.]