math Puzzler..


This is just a question that has stumped me for some time:

We have a normal watch.
The big hand is 4cm long and the little hand is 3cm long.
What's the distance between the tips of the hands at the moment they are moving the fastest towards each other.

5 cm. Think out why.

Facinating question. I don't get it? Say the clock was 20 feet in diameter. Please enlighten me.

is that the moment of change between obtuse and acute exchange between the angles at the tips? (assuming a triangle ascribed by the hands)

Of course, the hands never actually move "toward each other" as they are travleing in the same direction,(yes?) but the speed of aproach and recession for he points of the hands does, and is a great question. :)

Bob: the first thing that jumped out at me when you said 5 was the 3-4-5 triangle being involved and it is almost a 'trick' question... with no difficult forumulas needed. I'll think on that, thanks for the hint

Lance: the size of the clock face itself wouldn't matter because what we are after is the relationship between the two hands (the lengths of which we are given).

Ken: Theats right. they are always moving in the same direction.. I was thinking rates of change, but I had no function to start with so I didn't know where to start :(

Thanks for the responses everyone...

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