Answer to the Problem of the Week
for the week of February 21, 2005

The Bigger Burger Problem

There are three high schools located in the diagram below:
Handley is located at (-4, 3);
Sherando is located at (2, -5); and
Millbrook is located at (6, 5).

The Winchester Bigger Burger wants to build a new restaurant that is centrally located so that it is the same distance from each of the three high schools.   Distance is measure along North-South and East-West gridlines -- NOT as the "crow flies."

Where should the Bigger Burger locate?

Picture of 3 high schools

 

Solution to the Problem:

The answer is (2, 2)
In the diagram below, I located the points which are equidistant from Handley and Millbrook (shown by the path marked in this color). Then I located points which are equidistant from Millbrook and Sherando (shown by the path marked in this color).

position of bigger burger
Gilbert Melanson sent in an excellent algebraic analysis of this problem.
To see it, click here.

Correctly solved by:

1. Jeffrey "The Yellow Dart" Gaither Winchester, Virginia
2. Trey Mason Winchester, Virginia
3. John Funk Ventura, California
4. Richard Johnson La Jolla, California
5. Chris Rogers Winchester, Virginia
6. Larry Schwartz Trumbull, Connecticut
7. Arsalan Heydarian Harrisonburg Virginia
8. Jason LaRusso Winchester, Virginia
9. Tarpley Ashworth Harrisonburg, Virginia
10. António Baptista Lisboa , Portugal
11. Jim Kennedy Limerick, Ireland
12. James Alarie University of Michigan -- Flint,
Flint, Michigan
13. Gilbert Melanson Sierra Vista, Arizona
14. Cameron S. Columbus, Georgia
15. Ben Swartz Winchester, Virginia
16. Jaime Garcia Virginia Tech,
Blacksburg, Virginia
17. John Harcourt Columbus, Georgia
18. Wajih Ansari Harrisonburg Virginia
19. Justin Crabill Harrisonburg Virginia
20. Tom Robb Winchester, Virginia
21. Weimers Winners Lordstown, Ohio
22. Angelo Leone Middletown, Connecticut
23. David & Judy Dixon Bennettsville, South Carolina
24. Kirstine Wynn St. Olaf College,
Northfield, Minnesota
25. Mac Dillon Columbus, Georgia
26. Sam Coffin Columbus, Georgia
27. Kevin Jacobson Columbus, Georgia
28. Cameron Burkholder Winchester, Virginia
29. Sheila Shah Arlington, Virginia
30. Tristan Collins Winchester, Virginia
31. Walt Arrison Philadelphia, Pennsylvania
32. Alex McIntire Columbus, Georgia
33. Paige Janke Columbus, Georgia