Answer to September 1, 2003 Problem

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