Velocities moving against each other cancel each other out. What is the velocity of an airplane that flies at 500 mph and then encounters a 50 mph headwind (wind going against the direction of the plane)?

the kind of relationship between atmospheric  density and altitude is inverse relationship. this means a surge in either will cut the other factor. density is mass per unit volume, it is hard to compute with only altitude 1,291 kilometers given. also, we could also use temperature and pressure to resolve density but they are not delivered.