Help me with some basic algebra

[troopernflight]

I've been looking at something for 3 hours on Pilot's Web in regards to time/distance to station computations, and my brain is fried.

Using the One to Sixty Rule, it says:
Distance between bearings / Distance to the station is proportional to Degrees between bearings / 60.

It further explains that the "Distance between bearings" is a fuction of the aircraft's speed and lapsed time:
(a) Speed=Distance/Time.

They break it down by using basic algebra into:
(b) Distance between bearings= Speed / 60 * Minutes

Combining a and b forms the final formula:
Distance to station= TAS * Minutes flown / Degrees between bearings

I know I can just memorize this formula, but I'm trying to understand how it was derived from the original One to Sixty Rule. I really struggle with understanding math. A gold star to anyone who can explain this in terms I can understand.

 

[Dugie8]

Rule of 60. At 60 NM 1 degree is 1 NM.

You are 60 NM from a VOR on the 090 radial (lets say outbound) you turn and fly 360 (assuming no declination on the VOR) in 1 minute you are on the 088 radial, your ground speed is 120 knots.

Using your (b) formula. speed = (distance between bearings) * 60 * minutes (speed = 2 *60 * 1)= 120

OR further applying the rule of 60

At 60 knots (ground speed) you are traveling 1 NM/minute (at 120 its 2, at 30 its .5, etc).

 

[pwapilot]

A complete derivation of that formula and the "Rule of 60" involves some trigonometry and a few approximations. I happen to have wrote a derivation from when I first saw that formula during my instrument training a few years ago (and was wondering where it comes from as are you); see the attached PDF.

 

[troopernflight]

Awesome. Thanks for that explanation! I had to brush up on my trig a little before I could understand it. Brought back old memories with the Soh-Cah-Toa mnemonic. Sin=Opposite/Hypotenuse, Cos=Adjacent/Hypotenuse, Tan=Opposite/Adjacent.