Dry Gulch Treasure

"Desert Road and Mountain Road intersect at right angles in downtown Dry Gulch. On Desert Road, within 10 miles east of this intersection grows the old hanging tree (H). Within 10 miles west of the intersection on Desert Road is the old well (W). On Mountain Road, within 10 miles north, there is the stagecoach stop (S) in one place and Barry's Farmhouse (F) in another spot. Draw a first line from H to F and a second line from W to S. These two lines intersect at Magic Point A. Draw a third line from H to S and a fourth from W to F; they cross at Magic Point B. The treasure is buried at the point where line AB crosses Desert Road."

I went searching for the treasure. I found the hanging tree 3 miles east of town and the well 6 miles west of town. But there was no longer any sign of the stagecoach stop or of Barry's farmhouse. Yet, I was able to find the exact location of the treasure. Where was it?

Source: Internet newsgroup rec.puzzles. Used as Ken's POTD 11/14/94.

Upon receiving a few responses, I was asked what the solution would be if the distances to the hanging tree (H) and well (W) were variables. Is it only the ratio that's important, or are the absolute distances critical to the solution? Can someone provide a solution in terms of distances H and W?

The treasure is 12 miles east of Dry Gulch. Larry Baum's solution:

H is at (3,0), W is at (-6,0), F is at (0,f), S is at (0,s) for dome s &
f > 0.

Line HF: y = -f/3(x-3)
     HS: y = -s/3(x-3)
     WF: y = f/6(x+6)
     WS: y = s/6(x+6)

Then A = HF|WS = ( (6f-6s)/(s+2f), 3fs/(s+2f) )
     B = HS|WF = ( (6s-6f)/(2s+f), 3fs/(2s+f) )

For the line AB the slope computation is straightforward but tedious. 
It reduces to 
-fs/(6f+6s).

Hence line AB: y = [-fs/6(f+s)](x - (6f-6s)/(s+2f)) + 3fs/(s+2f)
                 = [-fs/6(f+s)]x + 2fs/(f+s)
                 = [-fs/6(f+s)](x - 12)

So when y = 0, x = 12.