Cowboy problem

stevecowall said:
A cowboy on a horse is 2 miles south of a stream that runs east to west. His ranch is x miles east and 5 miles south of his current location. The cowboy wishes to water his horse at the stram and then get to his ranch. Find the minum number of miles that this trip requires.
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Hello, stevecowall!

You could at least draw a diagram.
And beware of a sneaky fact . . .

A cowboy on a horse is 2 miles south of a stream that runs east to west.
His ranch is x miles east and 5 miles south of his current location.
The cowboy wishes to water his horse at the stream and then get to his ranch.
Find the minimum number of miles that this trip requires.
Click to expand...

Code: 
      : - -  x  - - :
      C     P       B
      *-----*-------*
      |    *  *     |
      |   *     *   | 2
    7 |  *        * |
      | *           *
      |*            A
      *
      D
The cowboy is at \(\displaystyle A\!:\;AB = 2,\;BC = x\)

His ranch is at \(\displaystyle D\!:\;CD = \) [COLOR=#b00e]7[/COLOR]

He rides to point \(\displaystyle P\) then to his ranch at \(\displaystyle D.\)

We want to minimize the distance \(\displaystyle \overline{AP} + \overline{PD}.\)
 
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