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.

430m is correct.

Let t signify the length of the track.

From the first meeting we obtain: 170/(1/2t-170) as the ratio of the runners' speed.

From the second, we obtain (t-90)/90 as the same ratio.

But if so, then 90*170=(t-90)(1/2t-170), or 30600=(t-340)(t-90), so t^2=430t, and t=430

Posted by broll on 2016-03-01 05:24:56