Question

What is the speed of a plane that travels at a rate of 410 mph with a wind of r​ mph?

Answer 1

The airplane's speed in the direction of its heading is
.. 410 mph +r*cos(θ)
where θ is the angle between the plane's heading and the direction the wind is moving toward.

That is, if the plane is moving "with the wind," its speed is (410 +r) mph.
If the plane is moving "against the wind", its speed is (410 -r) mph.