Problem:
Crystal has a running course marked out for her daily run. She starts this run by heading due north for one mile. She then runs northeast for one mile, then southeast for one mile. The last portion of her run takes her on a straight line back to where she started. How far, in miles, is this last portion of her run?
Answer Choices:
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Solution:
When Crystal travels one mile northeast she travels miles north and miles east. Similarly, when she travels southeast for one mile she travels miles south and miles east. Just before the last portion of her run she has traveled a net of miles north, and miles east. By the Pythagorean Theorem, the last portion of her run is
The problems on this page are the property of the MAA's American Mathematics Competitions