Answer to the Problem of the Week
for the week of December 12, 2005

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