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Like Clockwork (Posted on 2004-02-27) Difficulty: 4 of 5
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 Best and final | Comment 16 of 29 |
I GOOFED ,
In my last post which provided a fast but totally
wrong answer I started with a false statement:
" If distance increases most rapidly so does its square...". SAYS WHO??

GIGO* - ALL THE REST IS WRONG.
(* GARBAGE IN --GARBAGE OUT)

My reasessment is as follows:
for A=.001 to 1.7
evaluate D=((25-24cos(A+.0001))^.5 D=distance
DD=((25-24cos(A+.0001))^ .5 DD=D increased
rate= (DD-D)/.0001

Checking the table for max. rate and refining the
search in the neigborhood-we get nice and round numbers:

max rate= 3
distance= sqrt(7)
cos(angle)=3/4

This corraborates Charlies solution, however without referring explicitly to calculus-just examining the deltas' (=inreases) ratio.
ady



Edited on February 28, 2004, 9:02 am
  Posted by Ady TZIDON on 2004-02-28 08:56:55
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