Answer to May 21, 2001 Problem

The Pool Problem

 
As the Memorial Day Weekend approaches, swimming pools are being filled in anticipation of the first summer holiday.

At the local Winchester pool, a certain pipe can fill it in 2 hours. Another pipe can fill it in 5 hours. A third pipe can empty the pool in 6 hours.

With all three pipes turned on exactly at the same time, and starting with an empty pool, how long will it take to fill the pool?

 

Solution to Problem:

The answer is 1 7/8 hours.

In 1 hour, the first pipe fills 1/2 the pool, the second pipe fills 1/5, and the third pipe empties 1/6. That is, in 1 hour the pool fills:
1/2 + 1/5 - 1/6 = 15/30 + 6/30 - 5/30
= 16/30 = 8/15 of the pool.

For the whole pool to fill, it would take 15/8 or 1 7/8 hours.


Correctly solved by:

1. Renata Sommerville Austin, Texas
2. Keith Mealy Cincinnati, Ohio
3.Walt Arrison Philadelphia, Pennsylvania
4. Eric Harding Ashburn, Virginia
5. David Powell Winchester, Virginia
6. Joe Heintz Manchester, Tennessee
7. Izzy Kushner Closter, New Jersey
8. Kirstine Wynn Winchester, Virginia
9. Richard K. Johnson La Jolla, California
10. Mr. Bennington's Math 8 Classes High River, Alberta, Canada
11. Gusti Oggenfuss Montet, Switzerland
12. Ricki Stern Highland Park, New Jersey
13. Jason Farmer Winchester, Virginia
14. Herb Shaffer Chantilly, Virginia
15. Bill Hall Wellington, Florida
16. ---------- United Kingdom
17. Erin McGinnis Winchester, Virginia