A plane is flying due north at 325 km/h and encounters a wind from the south at 45 km/h. What is the plane's new velocity with respect to the ground in standard position?

The answers are 270 km/h at 90 degrees. I am trying to figure out how they got this answer.

Question

A plane is flying due north at 325 km/h and encounters a wind from  the south at 45 km/h. What is the plane's new velocity with respect to the ground in standard position? 

The answers are 270 km/h at 90 degrees. I am trying to figure out how they got this answer.

anonymous · Answer

That answer is wrong ... in a wind from the South, the airplane will go faster across the ground! (Northward, of course)