perplexus.info :: Just Math : On Track

On Track (Posted on 2016-02-29)

Alice and Betty start running in opposite directions along a circular track, each starting at opposite ends of a diameter of the circle. Each runs at a constant speed.

When Alice and Betty meet for the first time, Alice has run 170 meters.

They meet for the second time after Betty has run 90 meters past their first meeting point.

How many meters long is the track?

From Mensa Puzzle Calendar, 2016, by Mark Danna and Fraser Simpson, Workman Publishing, New York, puzzle for February 18.

Submitted by Charlie

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Solution: (Hide)

The first time Alice and Betty meet, their combined distances total half the length of the track. The next time they meet, their combined distances since the first meeting total a full length of the track, and therefore each runner ran twice as far between the two meetings as up to the time of the first meeting. At the time of the second meeting, therefore, Alice had run 2*170 = 340 meters since the first meeting. But this was 90 meters short (from Alice's perspective) of the first meeting place.
So she needed to go an additional 90 meters to get to the original meeting place, and the track is 340+90 = 430 meters in circumference.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Generalisation.	broll	2016-03-01 09:52:34
re: Misread the problem	Charlie	2016-03-01 07:27:05
Misread the problem	Steve Herman	2016-03-01 07:02:35
Solution	broll	2016-03-01 05:24:56
Some more?	armando	2016-03-01 02:09:44
re: Circular logic (spoiler)	Charlie	2016-02-29 21:49:52
Circular logic (spoiler)	Steve Herman	2016-02-29 18:38:23

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