Math Chat: Daylight Saving Time And Water Levels

Daylight Saving Time And Water Levels

Old time challenge.

John lives in an Atlantic coast state of the United States, and Mary lives in a Pacific coast state. When talking on the telephone from home recently, they realized it was the same time in both locations. How could this have been possible?

Solution

Florida and Oregon extend into the Central and Mountain time zones. Winners Timothy Clark, Mike Soskis, Chuck Gahr, and Eric Brahinsky explain that if John lives in Pensacola, in Florida's western panhandle, which is on Central time, and Mary lives in Ontario, in eastern Oregon, which is on Mountain time, their clocks usually would be one hour apart. On Oct. 27, for the hour following the turn-back from 2 a.m. daylight-saving back to standard time in the Central time zone, John and Mary would enjoy the same time in both locations. Other more imaginative entries brought in Texas, Mexico, Panama, South America, and Vietnam, not to mention Alaska and Hawaii, which unfortunately extend only five times zones west of the East Coast.

Battery question

(Thanks to Chuck Gahr.)

Batteries Inc. know that about one battery in a thousand is bad. They use a 99 percent accurate test on all their new batteries. If a battery tests bad, what is the chance it is bad?

Answer

Not 99 percent, but only about 9 percent. On average, in a thousand batteries, the one bad battery usually tests bad, but of the 999 good batteries, 1 percent or about 10 also test bad. So of the batteries that test bad, only about 1/11 or about 9 percent really are bad.

New water level challenge

(Thanks to Jeff Bradford.)

When you throw the anchor over the side of your boat, does the water level in the pond rise or fall?

When ice melts in a glass of warm water, does the water level rise or fall?

Send answers and new questions to:

Math Chat, Bronfman Science

Center, Williams College,

Williamstown, MA 01267

or by e-mail to:

Frank.Morgan@williams.edu

The best submissions will receive a copy of the classic book "Flatland," which helps explain higher dimensions.