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Math Help - math puzzle (snails in unit square)

  1. #1
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    math puzzle (snails in unit square)

    i found this problem in a book of math puzzles.

    There are 4 snails. Each snail is on one vertex of a unit square and they travel at unit speed in a cyclical order until they all meet. What is the distance traveled by each snail?

    i don't know how to start this problem.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by oblixps View Post
    i found this problem in a book of math puzzles.

    There are 4 snails. Each snail is on one vertex of a unit square and they travel at unit speed in a cyclical order until they all meet. What is the distance traveled by each snail?

    i don't know how to start this problem.
    By symmetry the snails are always at the vertices of a square which rotates and shrinks as they move.

    The result is that each snail is moving directly towards its target which is moving at right angles to it. So the range rate is constant at unit speed. As they start unit distance apart they take unit time until they meet and have moved unit distance..

    CB
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