## Pages

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 Web math-frolic.blogspot.com

## Monday, August 23, 2010

### 100-Meter Race Problem

Just a simple word problem to start the week off; adapted from "Futility Closet" (http://www.futilitycloset.com/2010/08/02/the-handicap/):

Michael challenges his brother Ryan to a 100-meter foot race. When Ryan crosses the finish line Michael has only covered 97 meters.
Michael challenges Ryan to a re-match, but this time Ryan has to start 3 meters behind the starting line.
Assuming the brothers run at the identical speed they did in the first race, who will win?

Or, if you want a bigger challenge, Matt Parker asks on Twitter recently:
"Is any number palindromic in bases 2, 3 and 5? I know @stecks checked up to a million. But still, it feels like there should be one..."
...have at it??? ;-)
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Solution (1st problem):
Ryan wins again. Ryan is able to cover 100 meters in the time it takes Zachary to run 97 meters. By starting 3 meters behind the starting line, Ryan will be dead-even with his brother at the 97-meter mark, at which point he (Ryan) will then pull ahead for the victory!