Answer to September 22, 2003 Problem of the Week

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

September 22, 2003 Problem of the Month

Correctly solved by:

September 22, 2003
Problem of the Month