A mountain climber is journeying up a mountain trail. He starts out with the sunrise, and gets to the peak just as the sun is setting. Throughout the day, he moves with inconsistent speed, slowing down to rest a few times.

He spends the night at the top, and in the morning sets out downward, reaching basecamp by nightfall. (Even though the going is easier, he stops a number of times to admire the scenery and rest.)

Is there an altitude on the mountain slope for which the climber was at that exact altitude at the same point during both days? Why or why not?

I feel like the wording of this problem can change the answer based on the interpretation of the piece, "same *point* during both days".

First, I believe that there is a general assumption that the climber used the same trail both days. With that assumption, then we move to the next variable in the question: (same point) If we believe that the phrase "same point" is a LOCATION, not time relevant, then the climber would be at the same location and the same altitude at any given point in each of the respective climbs. (Picture: draw a line and retrace it following it in reverse) At any point in the line it is on the exact spot of the first line drawn.

However, if the phrase "same point" is in reference to TIME during each of the trips, then assuming that the climber is inconsistent we cannot pinpoint an exact spot in which the climber will be at the same altitude at the same time on each of the days. We would have to assume the the mountain climber was traveling at the same speed, CONSISTENT, traveling up and down the mountain. And, because the climber is not climbing at the same speed, it is not possible.

Posted by O on 2003-05-09 22:10:56