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 Like Clockwork (Posted on 2004-02-27)
A clock's minute hand has length 4 and its hour hand length 3.

What is the distance between the tips at the moment when it is increasing most rapidly?

 See The Solution Submitted by DJ Rating: 4.0000 (9 votes)

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 solution (seems too simple) | Comment 4 of 29 |
The fact that both hands are moving is irrelevant. In other words the answer is the same if you say decreasing instead of increasing. You have a triangle with two known side lengths. The question is at what angle between the know sides would changing that same angle by a fixed amount cause the greatest change in the length of the third unknown side. The answer is when the shorter known side is at 90° to the unknown side. If the known sides are equal the answer is 0. With sides of 3 and 4 the answer is the square root of (4²-3²) or 2.64575
 Posted by Dan Porter on 2004-02-27 15:49:39

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