Answer to September 22, 2003 Problem

"Old Faithful" Problem

The average interval between eruptions of "Old Faithful" is 94 minutes. An eruption lasts 1.5 to 5 minutes.
Castle Geyser at Yellowstone National Park erupts every 12 hours while Cliff Geyser erupts every 35 minutes.

If all three geysers erupt at the same time, how many days would elapse until the next time that they all erupt at the same time?

 

Solution to the Problem:

The answer is 236,880 minutes or 3,948 hours which equals 164.5 days.

You need to find the least common multiple of the three periods:
94 minutes, 35 minutes, and 720 minutes.

Factoring each of these three numbers,
94 = 2 x 47,
35 = 5 x 7, and
720 = 2 x 2 x 2 x 2 x 3 x 3 x 5.

Hence, the LCM would equal
2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 47 or 236,880 minutes.
Dividing by 60 yields 3,948 hours, and dividing by 24 gives the answer of 164.5 days.


Correctly solved by:

1. Akash Patel Columbus, Georgia
2. Walt Arrison Philadelphia, Pennsylvania
3. Bill Funk San Antonio, Texas
4. Richard Johnson La Jolla, California
5. Rick Jones Kennett Square, Pennsylvania
6. John Funk Ventura, California
7. James Alarie University of Michigan -- Flint
Flint, Michigan
8. Jim Kennedy Limerick, Ireland
9. Chris McCormick Winchester, Virginia
10. Nate Wilson Winchester, Virginia
11. Jeffrey Gaither Winchester, Virginia
12. David & Judy Dixon Bennettsville, South Carolina
13. Ashley Neumann Winchester, Virginia
14. Le My An Ho Chi Minh City, Viet Nam
15. Keith Mealy Cincinnati, Ohio
16. Michael Jacobs Winchester, Virginia
17. Laura LaRusso Winchester, Virginia
18. Ashleigh Rogers Winchester, Virginia
19. Franklin Harcourt Columbus, Georgia
20. Misty Carlisle Winchester, Virginia
21. Frank Sitarski Plainville, Massachusetts
22. Evelyne Stalzer Montville, New Jersey