September 1, 2003
Problem of the Month

Train Problem

Out west, there are long stretches where Interstate 80 runs parallel to the Union Pacific railroad track.   Last summer, I set my car on cruise control at 64 m.p.h.   It took me 34 seconds to pass a 900 foot long train (i.e., it took 34 seconds from the time my car caught up to the end of the train until it pulled even with the front of the train).

If both the train and car moved at constant rates of speed, how fast was the train going?

How far did the car travel before it overtook the train?

Solution to the Problem:

The answers are 45.95 mph and 3,191 feet.

Let D = the distance in feet that the train travels until the car catches up.
Then the car would have traveled D + 900 feet.
Both the train and the car travel for 34 seconds.
Let y = the rate of the train.

From this information, you can fill in the following table:

	Rate (in mph)	Time (in hours)	Distance (in miles)
Car	64 mph	34/3600 hr	(D + 900)/5280 miles
Train	y mph	34/3600 hr	D/5280 miles

Since (Rate) x (Time) = Distance, we can set up the following equations and solve:

Correctly solved by:

1. Walt Arrison	Philadelphia, Pennsylvania
2. Lucy Flournoy	Columbus, Georgia
3. Rick Jones	Kennett Square, Pennsylvania
4. Richard Johnson	La Jolla, California
5. Tomas Grahn	Tullängsskolan, Örebro, Sweden
6. V. Karlsson and P. Sundberg	Tullängsskolan, Örebro, Sweden
7. James Alarie	University of Michigan -- Flint Flint, Michigan
8. Karl Larsson	Tullängsskolan, Örebro, Sweden
9. Chris McCormick	Winchester, Virginia
10. Matt McMurtry	Arlington, Virginia
11. Bill Funk Jr.	San Antonio, Texas
12. David Hill	----------
13. Viktor Bergqvist	Tullängsskolan, Örebro, Sweden
14. Jeffrey Gaither	Winchester, Virginia
15. Geoff Keith	Santa Monica, California
16. Nate Wilson	Winchester, Virginia
17. Kathryn Harris	Winchester, Virginia
18. Hank Warren	----------
19. Jeremy Ferguson	----------
20. Jaime Garcia-Ramirez	Winchester, Virginia
21. David Wong	Winchester, Virginia
22. Laura LaRusso	Winchester, Virginia
23. Patrick Wingfield	Winchester, Virginia
24. Shannon Bagshaw	Winchester, Virginia
25. Cady	Columbus, Georgia
26. Nina Karlsson	Tullängsskolan, Örebro,Sweden
27. Greg Gaynor	Winchester, Virginia
28. Riley Prescott	Columbus, Georgia

The following solved one part of the problem:

29. Jim Kennedy	Limerick, Ireland
30. Chris Moats	Winchester, Virginia
31. David and Judy Dixon	Bennettsville, South Carolina
32. Ashley Neumann	Winchester, Virginia
33. Cameron Emmart	Winchester, Virginia

Send any comments or questions to: David Pleacher