Math makes my so-called brain ache. I can do it, but it takes a lot of effort.

Easier to ask if anybody else has ever checked this formula than to pencil it
out myself and probably make mistakes.

This would be a handy formula is known to be true, or even a close
approximation.
Useful for short legs when dead reckoning.

"Every three minutes, a boat will travel 100 yards x the speed in knots."
The rule of thumb would obviously disregard variables like, wind, current,
tracking error, and so forth..............but as for the premise itself.....

Always true?
Never true?
True only at certain speeds?........(not likely, would probably work at a
variety of speeds since the time and distance are in consistent proportion)