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The Oil Problem

Posted by ragknot on December 13, 2012 – 11:30 pm

An oil well being drilled in flat prairie country struck pay
sand at an under ground spot exactly 21,000 feet from one corner of a rectangular plot of farmland, 18,000 feet from the opposite corner, and 6000 feet from a third corner.

How far is the underground spot from the fourth corner ?


This post is under “Tom” and has 8 respond so far.
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8 Responds so far- Add one»

  1. 1. DP Said:

    There are two answers I can find to this problem.
    If by opposite you mean diagonally opposite, then the answer is 27,000 feet.
    If by opposite you mean share a common side of the rectangle, then the answer is 12,369. The only way for this to happen is if the 21,000 and 18,000 corners share a side of the rectangle, and so do the 18,000 and 6,000 dimensions. It is not possible for the 21,000 and 6,000 dimensions to share a side and the point be 18,000 feet from another corner.
    I suspect you were looking for the 27,000 feet.

  2. 2. Chris Said:
    
    o   a    o           c           o
    d                                d
    o        X                       o 
    
    b                                b
    
    o   a    o           c           o
    

    Let the origin be at the bottom left corner of the rectangle, i.e. (0, 0)
    Let the spot be at (a, b).
    Let the top left corner be at (0, b+d).
    Let the bottom right corner be at (a+c, 0)
    Then the top right corner is at (a+c, b+d)

    I’ll use units of 1000 feet. We have:

    {E1} a² + b² = 18²
    {E2} c² + d² = 21²
    {E3} a² + d² = 6²

    We want to find x, such that x² = b² + c²

    {E1} + {E2} => (a² + b²) + (c² + d²) = 18² + 21²
    = (b² + c²) + (a² + d²) = x² + 6²
    => x² = 18² + 21² – 6² = 729 = 27²
    So x = 27 (thousand) feet

    If I’d used the bottom right corner, rather than the top left corner, as being
    the one that was 6 (thousand) feet from the spot, I get the same result

  3. 3. ragknot Said:

    Correct 27000

    This was added to ToM many years ago. But I don’t know who did it right, then.

  4. 4. abhay Said:

    I have 2 answers
    1.27000
    2.13000

  5. 5. Dusty Said:

    Well according to the people above I’ve done something wrong in my math, but, I believe the correct answer to be 28,301.943 ft. Quite a brain twister! THANKS!!

  6. 6. Chris Said:

    I had assumed that the spot was inside the rectangle. If it is outside, you still get 27,000 feet for the last distance.

  7. 7. DI Said:

    Simple logic states that if it is any distance from 3 corners and it is a rectangle, Then the spot itself would be the 4th corner.

  8. 8. Chris Said:

    Hi DI. No it doesn’t. See my post (2) for how to do it.

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