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Feet Per Minute

I recently have found a new hobby:
Geocaching.
I've been wondering just how precise a GPS receiver can get (assuming
perfect reception).
Latitude and Longitude are measured in degrees, latitude measured North or
South from 0 to 90 degrees, longitude measured East or West from 0 to 180
degrees. Each degree is divided into 60 "minutes". Each minute is
divided into 60 "seconds", though most displays of coordinates just break
the minutes into three decimal places, like "N 38 degrees, 47.213 minutes".
Assuming the Earth is a sphere with a circumference of 25000 miles,
how many feet are in each minute? And thus, how precise is a thousandth of
a minute?
The answer for latitude is constant, but the answer for longitude will vary
with the latitude. (At the poles, no distance is traveled for a change in
longitude.) Can you find a formula for both? Feel free to send
URLs of web references, too.

Source: Original.

Solution

Mail to Ken