Red car wants to pass Blue car in front of him, but to do so will need
to cross temporarily into the lane of opposing traffic.  Out at a
distance, there's a truck coming towards him in the opposing lane.

What is the mathematical formula to figure how fast Red car needs to
drive in order to make the pass, assuming Blue car is driving at x
speed, and the truck is approaching from y distance and travelling at
z speed?

You also need to know how much distance is allowed between cars (when
red is passing blue and between red and the truck) and how far the car
travels when changing lanes (or are we assuming an instantaneous lane
change?)

to keep more simple assume an instantaneous lane change. as far as the
distance between red and truck it's a variable in the equation,
regarding distance between cars, assume an average car length, and the
issue of how far the car travels when changing lanes I'm not sure what
to do with, maybe assume he cuts blue off and gets right back into his
lane at the earliest possible moment.

thanks!!

OK, I quite like this question so I thought I'd give it a go. No
guarantees for correctness (normal, as I don't get paid!).

I have redefined your question as follows, including a safety distance
'k' which is being respected by A from B at time=0:
      |---------y---------------C
A--k--B

And respected by A from B AND C at time=t:
             |--k--A--k--|C
      |---b--B

[Remembering that speed = distance/time (s=d/t)]
The combined distance covered by B & C in time t is y-2k, and from
s=d/t we get d=ts so this is equal to tx + tz.
Thus y-2k=tx+tz
Rearrange to t=(y-2k)/(x+z) which gives us the time t at which A
should be at overtaking point.
The distance travelled by B in this time (from d=st) b = x(y-2k)/(x+z)
If B has travelled distance b, A must travel k + b + k = b+2k 
Substituting our value for b gives: x(y-2k)/(x+z) + 2k 
Put over a common denominator: 
x(y-2k) + 2k(x+z)
-----------------
     (x+z)

The speed of A is this distance divided by the time t:
  x(y-2k) + 2k(x+z)
  -----------------
       (x+z)
---------------------
       (y-2k)
  -----------------
       (x+z)

which simplifies to:
  x(y-2k) + 2k(x+z)
---------------------
       (y-2k)

or x + 2k(x+z)/(y-2k)

(One could also complicate matters further by showing that the
distance AC should be greater than the distance AB because the
difference in speed is greater...)

cool, thanks!