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.

Let t denote the length of the track, and a and b the distances travelled by the runners, as above.

Then a/(1/2t-a) = (t-b)/b

2ab=(t-b)(t-2a)

t^2-2at-bt=0

t^2=t(2a-b)

t=2a-b.

Always true, under the given conditions.

Posted by broll on 2016-03-01 09:52:34