# math

Boris and Stella are running on a circular track which has a
radius of 300 meters. They start running at the same time.
Boris starts at the northernmost point of the track, and
Stella starts at the easternmost point. Boris runs clockwise.
Stella runs counterclockwise, and she runs twice as fast as
Boris runs. They pass each other for the first time after 85
seconds. How far apart are Boris and Stella when they
have been running for 800 seconds?

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1. They are 1/4 of a circle apart to begin.
Boris runs 1/12 of a circle and Stella runs 1/6 of a circle in 85 seconds.
So, Boris's angular speed is ω = 2π/85 and Stella's speed is 4π/85
So, at time t,
Boris's location is (300 sin 2π/85 * 800, 300 cos 2π/85 * 300)
Stella's location is (300 cos 4π/85 * 800, 300 sin 4π/85 * 300)
So just use the distance formula to get the answer.

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