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?

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

(In reply to Misread the problem by Steve Herman)

Coincidentally that's what happened to me when this first came up on my calendar. I misread the problem and was surprised by the solution on the back; my solution had been the same as what you had posted, until I read the back of the calendar page; then I realized the two started at opposite ends of a diameter. That made me think this was a good puzzle for perplexus.

Edited on March 1, 2016, 7:37 am

Posted by Charlie on 2016-03-01 07:27:05