The cog railway at Pike's Peak leaves the station in Manitou Springs at an altitude of 6,571 feet and climbs to an altitude of 14,110 feet at its summit. The average grade is 16 percent. Determine the total length of the track from the station to the summit and compute the angle of elevation (using a 16% average grade).
Solution to Problem:
The total amount of track is 14,718 feet or 9.03 miles and the angle of elevation is 9.09 degrees.
Since the vertical gain is 7,539 feet (found by subtracting
6,571 from 14,110), you can find the horizontal distance (if it
were thought of as a right triangle) by dividing .16 into it.
So the horizontal change is 47,118 feet. Then using the Pythagorean
Theorem, the total amount of track would be 47,718 feet or 9.03 miles
(the Pike's Peak website lists the actual amount of track as 8.9 miles and the
average grade as 15%). The angle of elevation is found by taking
the inverse tangent of 0.16, which is 9.09 degrees.
Correctly solved by:
| 1. Charity Calhoun | Columbus, Georgia |
| 2. Joe Jenkins | Winchester, Virginia |
| 3. David and Judy Dixon | Bennettsville, South Carolina |
| 4. Richard K. Johnson | La Jolla, California |
| 5. Walt Arrison | Philadelphia, Pennsylvania |
| 6. Keith Mealy | Cincinnati, Ohio |
| 7. Jerry Putt | Loudoun County, Virginia |
| 8. John Funk | Ventura, California |
| 9. Joe Heintz | Manchester, Tennessee |
| 10. Nick Von Keller | Winchester, Virginia |
| 11. Matt Crandell | Winchester, Virginia |
| 12. Janine Oliver | Winchester, Virginia |
| 13. Lee Leonard | Winchester, Virginia |
| 14. Elizabeth Emmart | Winchester, Virginia |
| 15. Ellen Sankovich | Winchester, Virginia |