The best range IAS, Vbr,
does depend on the wind.
Loads has been written on this topic (
Prof. Rogers etc) but basically the way this works is that if you have a tailwind, you need to fly slightly slower than Vbr in order to take maximum advantage of the tailwind, and if you have a headwind then you need to fly slightly faster than Vbr in order to spend less time in the headwind.
The exact amounts of "slower or faster" depend on the combined gradients of the engine's specific fuel consumption v. power curve and the L/D curve. This Q cannot be answered because neither we, nor I suspect the OP, have any idea what this is.
For any normal gliding aircraft, the best range speed is theoretically equal to Vbg - the best glide speed. Obvious really
And every aircraft is a glider. An engine merely gives you the option of a positive rate of climb.
For a powered aircraft, this doesn't quite work because it assumes engine efficiency is constant over the power setting, which is obviously not going to be the case because the pumping and friction losses are largely constant so - assuming LOP operation - low power settings will be less efficient and thus Vbr will be higher than Vbg. On my TB20 Vbg is ~ 95kt but Vbr is about 110kt (still very slow!).
It is possible that if you have a 20kt tailwind you need to fly 10kt slower but there is no such rule; this would be a pure coincidence. I actually very much doubt it would be that much because if Vbg was say 60kt (IMHO pretty slow but possible) then 50kt will yield a pretty large AoA. I'd say the IAS adjustment will be a few kt at most for a talwind. But it could be a lot more for a strong headwind because one can so rapidly reach a situation where one is going literally nowhere and looking at the limiting case of say Vbr being 60kt and the headwind being 59kt, it is obvious that full power will be the optimal power setting regardless of efficiency. But as I say this is type specific.