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Length of Pole | 29 Sep 2009

Discussion in '$1 Daily Competition' started by shabbir, Sep 29, 2009.

  1. shabbir

    shabbir Administrator Staff Member

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    Pole is in a lake. Half of the pole is under the ground, One-third of it is covered by water. 8 ft is out of the water.

    What could be the possible length of the pole?
     
  2. sameer_havakajoka

    sameer_havakajoka New Member

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  3. sameer_havakajoka

    sameer_havakajoka New Member

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    48ft is correct

    Solution:

    Fraction of pole in the ground = 1/2
    Fraction of pole covered by water = 1/3
    Fraction of pole in the ground and covered by water = 1/2 + 1/3 = (3 + 2)/6 = 5/6
    Fraction of pole out of water = 1 - 5/6 = 1/6
    Thus, one-sixth of the pole (out of water) is 8 ft.
    So, total length of pole = 48 ft.

    It may be noted that:
    Length of pole in the ground = 48/2 = 24 ft.
    Length of pole covered by water = 48/3 = 16 ft.
    Length of pole out of water = 8 ft.


    The problem may also be solved by setting up the following equation: x/2 + x/3 + 8 = x
    where x denotes the total length of the pole in ft.
    The equation may be solved as shown below.
    5x/6 + 8 = x
    8 = x - 5x/6 = x/6
    x/6 = 8 or x = 48.
     
  4. shabbir

    shabbir Administrator Staff Member

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    Bingo
     
  5. sameer_havakajoka

    sameer_havakajoka New Member

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    yeyeyey, thanks sab.
     

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