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Sprinting around

Three amazing sprinters just started running around a circular track that is 400 yards in distance. Sonic the hedgehog and the Road Runner began at the starting line by running in opposite directions, with Sonic running clockwise and the Road Runner running counterclockwise. The Tasmanian Devil began at the point exactly halfway around the track from Sonic and Road Runner, and he began by running clockwise. They all started at the same time. Now, each time two runners meet, they immediately turn around and run the other way. Each of them runs at a constant speed of fifty yards per second (even while changing directions). How long will it take until the thirtieth meeting occurs? Which runners will meet for this thirtieth meeting?

How would your answer change if the Road Runner ran 80 yards per second?

(Source: Adapted from Mathematics Teaching in the Middle School, Jan 1998)

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