Answer to November 25, 2002 Problem

The Painting Problem

 
A painter needed 3 days to paint a room. He painted the four walls and the ceiling. Working at the same rate, how long would it take him to paint a room twice as long, twice as wide, and twice as high?

 

Solution to the Problem:

It would take 12 days.

Let x and y represent the length and width of the original room and let z represent the height.
The surface area of the original room would be given by:
A = 2xz + 2yx + xy.
The surface area of the larger room would be given by:
A = 8xz + 8yx + 4xy, which is four times as large as the original.


Correctly solved by:

1. Jeffrey Gaither Winchester, Virginia
2. Xiao Ma Columbus, Georgia
3. John C. Funk Ventura, California
4. Kathleen Altemose Winchester, Virginia
5. Elizabeth Harp Columbus, Georgia
6. Daniel Wilberger Winchester, Virginia
7. Walt Arrison Philadelphia, Pennsylvania
8. Gusti Oggenfuss Montet (Broye), Switzerland
9. David and Judy Dixon Bennettsville, South Carolina
10. Ashley Neumann Winchester, Virginia
11. George Gaither Winchester, Virginia
12. Natalie Frisén
      Lotta Österberg 		Örebro, Tullängskolan, Sweden
13. Lina Öijerholm
      Tove Westlund 		Örebro, Tullängskolan, Sweden
14. Jimmy Careliussèn Örebro, Tullängskolan, Sweden
15. Jan-Erik Kylänpää Örebro, Tullängskolan, Sweden
16. Fredrik Simón Tullängen Örebro, Sweden
17. Daniel Carlén Tullängskolan, Sweden
18. James Alarie Univesity of Michigan -- Flint
Flint, Michigan
19. Matt Stillwagon Winchester, Virginia
20. Keith Mealy Cincinnati, Ohio
21. Peggah Sadeghzadeh Winchester, Virginia
22. Rich Murray Ridgetown, Ontario, Canada