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*From*: Brian Whatcott <betwys1@sbcglobal.net>*Date*: Fri, 14 Aug 2009 11:54:49 -0500

You are probably familiar with a puzzle which is usually tricked out

with plausible numbers which conjure an image of a bird/fly/insect

flying repeatedly between two trains approaching each other

on the same line.

This may be expressed as

train1 speed x mph train2 speed y mph bird speed z mph

Trains' starting separation a miles.

Question: How far does the bird travel between the two trains

before they collide?

This can be a vivid illustration of the benefit of a little analysis

in avoiding extended calculations, which goes like this:

joint speed x + y mph; time to collide a/(x+y) hours;

therefore....

Distance flown by bird; z.a/(x+y) miles

There is a comparable puzzle called four birds in a square field.

If each bird sets off at the same time, and aims for the next bird in

clockwise progression, how far does each bird fly before the birds collide?

For a square of side a miles, and an airspeed of x mph,

the mutual curvilinear approach speed this time is just x mph - because the target

always flies orthogonally.

Therefore...

Distance flown by a bird is a miles.

There is a third variation, which goes like this:

There is a bird at the corner of an equilateral triangular field of side a miles.

If each bird sets off flying at x mph at the same time, and aims directly for the next bird in clockwise progression, how far does each bird fly before the joint collision?

The method should not take a giant leap of intuition, if it is prepared by these prior examples....

Brian W

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