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An inconsistent climber (Posted on 2002-04-25) Difficulty: 2 of 5
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?

  Submitted by levik    
Rating: 3.3000 (10 votes)
Solution: (Hide)
Let's call our climber "Bill". Imagine a climber "John coming down the mountain in the same exact way that Bill comes down it, but a day earlier.

In other words, John is coming down the mountain on the same day as Bill is ascending it. Now with Bill going up, and John going down, the two men will be on the same altitude at some point in the day.

Because Bill going down and John going down will follow the same path, John will, at that poing, be at the same altitude as Bill will be in 24 hours. So, that is the point in time that Bill is at the same altitude on both the days.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionNo SubjectK Sengupta2007-04-01 15:14:32
Some ThoughtsCommentOld Original Oskar!2005-02-22 11:02:28
Great PuzzleBruce Brantley2004-08-22 19:46:57
kela!rajesh2003-07-10 20:53:01
how about this?rajesh2003-07-10 20:51:00
regarding my previous postingO2003-05-09 22:15:57
re: inconsistent climberO2003-05-09 22:10:56
re: inconsistent climberGamer2003-03-09 14:19:36
re: inconsistent climberDan2002-09-07 17:39:52
inconsistent climberJasper2002-04-25 11:45:58
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