Question

A pilot is flying at a speed of 300 miles per hour and the wind is blowing due north at 50 miles per hour.What is the magnitude of the resultant velocity of the plane?

Answer 1

depends on which direction the plane is heading. The speed could be anywhere between 250 and 350 mph.

Answer 2

300 mph on what heading?

Usually you give the direction a wind is coming from, like a North wind caries you south.
Here do you mean it blows you North?

In any case use vector components
North component = 50 + 300 cos A
East component = 300 sin A
where A is the heading angle clockwise from north

magnitude = sqrt(north comp^2+east comp^2)