## 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 ?

December 14th, 2012 at 11:20 am

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.

December 14th, 2012 at 3:02 pm

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

December 14th, 2012 at 11:58 pm

Correct 27000

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

December 21st, 2012 at 7:06 am

I have 2 answers

1.27000

2.13000

December 27th, 2012 at 3:00 pm

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!!

December 28th, 2012 at 7:53 am

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

February 2nd, 2013 at 1:25 pm

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.

February 2nd, 2013 at 9:31 pm

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