December 12, 2005
Problem of the Month

The Temperature Problem
from Car Talk

Kate is heading off to work one fall morning, and as she does every morning, she passes a billboard that displays the current temperature in Fahrenheit in one corner, and the temperature in Celsius in the other corner.

She notices both temperatures, and thinks, 'It's a pretty nice day for late fall.'   But, as the day progresses, a monstrous cold front hits town.   On her way home, Kate passes the temperature billboard again, and finds that the Fahrenheit temperature is now 36 degrees colder than it was that morning.   So, when she drove in it was one temperature, and now it's that temperature minus 36.

But, when she looks at the Celsius temperature she's confused, because it reads exactly the same as it did that morning.   Then Kate figures that the negative sign must be burned out in the display.

How cold was it?

Solution to the Problem:

The temperature must be 14 degrees Fahrenheit or -10 degrees Celsius.

Earlier, it had been 50 degrees Fahrenheit or 10 degrees Celsius.

Let F = 9/5 C + 32, where F and C represent the earlier readings.

Then F - 36 = -9/5 C +32 at the later time.

Solving these two equations, we get:
2F - 36 = 64
Therefore, F = 50 degrees
and F - 36 = 14 degrees.
C = 5/9 (F - 32) yields the Celsius temperatures.
C = 5/9 (50 - 32) = 10 degrees.
C = 5/9 (14 - 32) = -10 degrees.

Correctly solved by:

1. Sagar Patel	Columbus, Georgia
2. Walt Arrison	Philadelphia, Pennsylvania
3. Jeffrey Gaither	University of Virginia Charlottesville, Virginia
4. William Proffitt	Winchester, Virginia
5. Jim Arrison	Norristown, Pennsylvania
6. Chris Rogers	Lord Fairfax Community College Middletown, Virginia
7. Suzie Chhouk	Long Beach, California
8. John Funk	Ventura, California
9. Richard K. Johnson	La Jolla, California
10. Keith Mealy	Cincinnati, Ohio
11. Tristan Collins	Virginia Tech Blacksburg, Virginia
12. Malin Fredriksson	Tullängsskolan, Örebro, Sweden
13. Maggie Morrison	Winchester, Virginia
14. Praveen Nandamuru	Columbus, Georgia
15. Tobi Kuforiji	Columbus, Georgia
16. Danny Gordon	Columbus, Georgia
17. James Alarie	University of Michigan -- Flint Flint, Michigan
18. Wictoria Widén	Tullängsskolan, Örebro, Sweden
19. Kunal Singh	Happy Valley, Shillong, India
20. Elias Hakuni	Tullängsskolan, Örebro, Sweden
21. Russell Beaty	Columbus, Georgia
22. Emily Sharrer and Simone Giovanetti	Harrisonburg, Virginia
23. Lauren Ko	Winchester, Virginia
24. Heather	----------
25. Carter Galbraith	Columbus, Georgia
26. Justin and Riaz	New york City, New York
27. Blake Hudson	Columbus, Georgia
28. Olivia Quach	Harrisonburg, Virginia
29. Gillian Grindstaff	Dallas, Texas
30. James P. Hus	Highland, Indiana
31. Stephen O'Hara	Winchester, Virginia
32. Bob Bardsley	Phoenixville, Pennsylvania
33. Evelyne Stalzer	Montville, New Jersey
34. Tom Robb	Winchester, Virginia
35. Ken Petersen	Mountain View, Wyoming
36. Erin Fennacy	Fresno, California
37. Kelley Kolar	Winchester, Virginia
38. David & Judy Dixon	Bennettsville, South Carolina
39. Zaza Carlzon	Tullängen, Sweden
40. Bharvi Desai	Columbus, Georgia
41. Andrew Montoya	Winchester, Virginia
42. Larry Schwartz	Norwalk, Connecticut
43. Emily Powell	Winchester, Virginia
44. Arin Smith	University of Virginia Charlottesville, Virginia

Send any comments or questions to: David Pleacher