Problem:
Keiko walks once around a track at exactly the same constant speed every day. The sides of the track are straight, and the ends are semicircles. The track has width meters, and it takes her seconds longer to walk around the outside edge of the track than around the inside edge. What is Keiko's speed in meters per second?
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Solution:
The only parts of the track that are longer walking on the outside edge rather than the inside edge are the two semicircular portions. If the radius of the inner semicircle is , then the difference in the lengths of the two paths is . Let be her speed in meters per second. Then , and .
The problems on this page are the property of the MAA's American Mathematics Competitions