In short, I need to know the relationship between volume, pressure,
and air compressors. Let me detail my question in the form of a
mathematical problem:

Suppose I have an air compressor that's rated to pump out 100 cu.ft.
per minute, and is rated at 90psi. The compressor is hooked up to a
tank whose capacity is 120 cu.ft.. At sea level, that tank already
contains 120 cu.ft. of air pressurized to 15psi (OK, 14.7psi, but
let's stick with easy numbers). The question is: How long will it take
that compressor to bring the storage tank up to 90psi?

I can think of 2 answers: (1) 1 minute OR (2) 6 minutes. Here's how I
arrive at each:

(1) 1 MINUTE:
At the start, the tank holds 120cuft @ 15psi. Since we're trying to
reach 90psi (or 6x atmosphere), that 120cuft would need to be
compressed to 20cuft to reach 90psi. 120cuft - 20cuft = 100cuft of
90psi needed. The compressor shoots out 100cuft/min @ 90psi, and
100cuft / 100cuft/min = 1min.

(2) 6 MINUTES:
The supposition here is that 100cuft is 100cuft, regardless of
pressure, and that the 90psi rating of the compressor in just a
maximum limit for the nozzle. To bring the tank to 90psi (6x
atmosphere), 6x the volume of air needs to be compressed into a 1x
space. In this case, the tank needs to have a total of 600cuft pumped
into it (120cuft tank x 6 = 720cuft - 120cuft present at start =
600cuft). Therefore 600cuft / 100cuft/min = 6 minutes.


I am leaning toward the idea that #2 is the correct answer. But would
somebody please clear up my confusion please? Thank you much.

What is the actual rating of your theoretical compressor:

The most common terms rating air flow capacity are ICFM, FAD, ANR, SCFM or nl/min  
There is no universal standard for rating air compressors, air
equipment and tools. Common terms are:

CFM 
ICFM 
ACFM 
FAD 
ANR 
SCFM 
nl/min 
CFM 
CFM (Cubic Feet per Minute) is the imperial method of describing the
volume flow rate of compressed air. It must be defined further to take
account of pressure, temperature and relative humidity - see below.
ICFM
ICFM (Inlet CFM) rating is used to measure air flow in CFM (ft3/min)
as it enters the air compressor intake .
ACFM
ACFM (Actual CFM) rating is used to measure air flow in CFM at some
reference point at local conditions. This is the actual volume flow
rate in the pipework after the compressor.
FAD
FAD (Free Air Delivered) is the actual quantity of compressed air as
measured at the discharge of the compressor at a specific pressure.
The units for FAD are CFM in the imperial system and l/min in the SI
system.
ANR
ANR (Atmosphere Normale de Reference) is quantity of air at conditions
1.01325 bar absolute, 20oC and 65% RH (Relative Humidity).
SCFM
SCFM (Standard CFM) is the flow in CFM measured at some reference
point but converted back to standard or normal air conditions
(Standard Reference Atmosphere) 14.4 psia, 80oF and 60% RH (Relative
Humidity).
nl/min
nl/min is the flow in l/min measured at some reference point but
converted to standard or normal air conditions 1.01325 bar absolute, 
0oC and 0% RH (Relative Humidity).

I'm not sure what all that means, but I will risk a suggestion.
I think you were on the right track at the start of both your calculations but for 
1) oversaw that on the way to compress the original 120 cft, you also
have to compress all the air that fills the tank to do so;
2) the tank needs to be filled to 6 times the volume, but one volume
is already there, so you need to pump in five more,
in either calculation, 5 x 120 cft = 600 cft => 6 minutes pumping.

BUT  - and this is where a researcher can provide an answer -
since the 90 psi is measured against the existing 15 psi in the
atmosphere, maybe the tank needs to be filled with 7 times the volume,
requiring 7'12" pumping time, whereby I also don't know if the
efficency of the pump declines as the pressure increase, so that the
time may be even longer.

I have talked myself into believing the 7 x volume, ...

Myoarin: Good point about loss of efficiency as pressure gets higher.
Presumably then the compressor needs to be higher than 90psi if I want
to pressurize the tank to 90psi.

Redhoss: I don't have many specifics on the compressor. All I'm given
is the CFM flow. So in my illustration I specified that the compressor
is rated at 100CFM.

WHAT IS THE POINT? The bottom line is I am trying to calculate how
long an air compressor on a locomotive would take to "charge the
system" -- ignoring leaks at the hose connections between train cars.
The supposition is that I know the total air capacity of each train
car, including brake pipe, brake cylinder, and air reservoirs. I am
just trying to figure out how air compressors will fill the brake
system.

xpnctoc-ga 

             I will not answer, since  imperial units give me headache,
but I will give you sufficient reference to underlying science:

1) Gas Law  (a search term) e.g.
http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm
will tell you how much gas you need in that tank to get that pressure

2) 'amount of gas' cannot be expressed as volume 
(litres or cubic feet) but as either mass or number od moles.
http://www.science.uwaterloo.ca/~cchieh/cact/c120/amounts.html


That applies to rating of the pump as well :
 It should be amount of gas delivered at given pressure.
 Rating you give may be interpreted that way (meaning at 90 psi it
will deliver amount which (at 90) would have that volume).

You may need R constant (to convert mols to grams) for air, it is given here:
http://www.grc.nasa.gov/WWW/K-12/airplane/eqstat.html

Rest is easy if you do it in standart units.

Hedgie