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Posers and Puzzles

Posers and Puzzles

  1. Standard member genius
    Wayward Soul
    06 Dec '03 16:32
    a man starts at the bottom of a hill at 7am, and gets to the top at 7pm. his speed varies. the next day he starts at the top at 7pm and gets to the bottom at 7pm. again, his speed varies. he takes the same route. prove that at one point during his return journey, he will be at the same point at the same time as the day before.

    some guy from my school at his interview for cambridge for maths a few years ago. the answer i've got is correct (it is!), but it could be explained better...i just can't think how to explin it better...:p
  2. Standard member kingofthe303
    Wormtongue
    06 Dec '03 18:16
    I think you have a typo in the Q. Otherwise the answer is stated in the question - he is at the top on both days at 7pm
  3. Standard member royalchicken
    CHAOS GHOST!!!
    06 Dec '03 20:34
    You're right, kingofthe303. Genius, just picture two people, one starting at one end at 7am and the other at the other. They both walk in opposite directions, at varying speed, reaching their respective goals at 7pm. Since it is obvious that they'll meet on the way (be at the same place at the same time), the desired result follows.
  4. Standard member genius
    Wayward Soul
    07 Dec '03 11:19
    Originally posted by royalchicken
    You're right, kingofthe303. Genius, just picture two people, one starting at one end at 7am and the other at the other. They both walk in opposite directions, at varying speed, reaching their respective goals at 7pm. Since it is obvious that they'll meet on the way (be at the same place at the same time), the desired result follows.
    yeah-that's the answer i had. although my maths teacher was arguing against it for a while...twas funny...and yeah-there was a typo-bottom at 7am day one and 7pm day two, and top at 7pm day one and 7pm day two...
  5. Standard member royalchicken
    CHAOS GHOST!!!
    07 Dec '03 20:32
    Originally posted by genius
    yeah-that's the answer i had. although my maths teacher was arguing against it for a while...twas funny...and yeah-there was a typo-bottom at 7am day one and 7pm day two, and top at 7pm day one and 7pm day two...
    What was your teacher's objection?
  6. Standard member genius
    Wayward Soul
    07 Dec '03 20:44
    Originally posted by royalchicken
    What was your teacher's objection?
    erm-i'm not exactly sure...he's really smart and a great teacher, i just think he was kinda taken aback...(it wasn't me that'd asked him, and the person that had tends not to shut up...)