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?

Well, I think if the climbing was graphed, we would find the answer. One graph could be time and location on the trail of the first climb. The second graph could be the time and location on the trail of the second climb. Put them both on the same piece of graph paper - there will be a point where the two line cross. This line will show when the climber was at the same altitude and the same place going up and coming down.

Posted by Jasper on 2002-04-25 11:45:58