Answer to the Problem of the Week
for the week of September 19, 2005
Contributed by James Alarie

Aging Problem

Anne's birthday was this summer (2005).   James immediately pointed out that she was aging more quickly than he was.   Seventeen years ago, James was three times as old as she was then.   Four years ago, James was just two times as old as she was.   In the year 2027, James will be only one and one half times as old as she will be then.

1. What are the current ages of James and Anne?
2. Since Anne is aging so much more rapidly than James, how long before they will both be the same age?

 

Solution to the Problem:

(1) James is 56 and Anne is 30.
(2) They will never be the same age.

Let x = James' age in 2005.
Let y = Anne's age in 2005.

Then we can write two equations:
x - 17 = 3 (y - 17)         <-- Seventeen years ago
x + 22 = 1.5 (y + 22)     <-- Twenty-two years from now (in 2027)

Solving simultaneously, we obtain:
x - 17 = 3y - 51
2x + 44 = 3y + 66

So, x + 61 = 117

Therefore, x = 56, and y = 30.

Correctly solved by:

1. David & Judy Dixon Bennettsville, South Carolina
2. John Funk Ventura, California
3. Mike Singer Winchester, Virginia
4. David McKinney Winchester, Virginia
5. Jeffrey Gaither University of Virginia
Charlottesville, Virginia
6. Tristan Collins Virginia Tech
Blacksburg, Virginia
7. Avery Acuff Columbus, Georgia
8. James Alarie University of Michigan -- Flint
Flint, Michigan
9. Malin Fredriksson Tullängskolan, Örebro, Sweden
10. Nate Troup Arlington, Virginia
11. Keith Mealy Cincinnati, Ohio
12. Samantha H. Washington Township HS, New Jersey
13. Maggie Morrison Winchester, Virginia
14. Misty Carlisle Cornell University
Ithaca, New York
15. Erin Fennacy Fresno, California
16. Rachel Pridgen Columbus, Georgia
17. Richard Johnson La Jolla, California
18. Ilir Dema Toronto, Ontario, Canada
19. Ben Swartz Stephens City, Virginia
20. Patrick McDuffee Harrisonburg, Virginia
21. Rich Murray Ridgetown, Ontario, Canada
22. Chris Rogers Winchester, Virginia
23. Sharina Smith Newport News, Virginia
24. Gusti Oggenfuss Centre de Rencontre
Montet (Broye), Switzerland
25. Charles Washington Winchester, Virginia
26. Julianne Harris Winchester, Virginia
27. Jessie Biggs Winchester, Virginia
28. Mary Bailey Wickham Columbus, Georgia
29. Anil Nataraj Columbus, Georgia
30. Praveen Nandamuru Columbus, Georgia
31. Olivia Quach Harrisonburg, Virginia
32. Sagar Patel Columbus, Georgia
33. Carter Galbraith Columbus, Georgia
34. Cerena Uttal Winchester, Virginia
35. John DeBergh Winchester, Virginia
36. Angie Cutshaw Williamsburg, Virginia
37. Walt Arrison Philadelphia. Pennsylvania
38. Zaza Carlzon Tullangsskolan, Örebro, Sweden
39. Wictoria Widén Örebro, Sweden
40. Gabrielle Groth Örebro, Sweden
41. Rickard Jansson Tullängsskolan, Örebro, Sweden
42. Krille Jansson Örebro, Sweden
43. Elizabeth Carlson Winchester, Virginia