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. From this information, you can fill in the following table:
Since (Rate) x (Time) = Distance, we can set up the following equations and solve:
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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 |