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.
Alicia and Betty meet at regular intervals. That means that every time they meet, no matter where they started from, they meet after Betty has run another 90 meters in one direction and Alicia another 170 in the other. So the track is 260 meters long.
Circular logic (spoiler)
