This is a simple question really but I just can't figure out what to do.

The question is as follows:

A small plane can fly at a speed of 200km/h in still air. A 30km/h wind is blowing from west to east. How much time is required for the plane to fly 500 km due north?

I was going on the rationale of time = distance/speed. The distance given is 500km.

I thought we could find the speed from pythagoras' theorem as sqrt (200^2+50^2) (as obtained from a vectorial representation), which for me, works out to 10*sqrt 409. So, I assumed that the answer was 50/sqrt(409) h. However, this is the wrong answer. You may immediately notice that this is wrong because by using this formula, we are believing that the plane flies north east, however, the questions asks for the time it takes to fly north.

How do I get the correct answer and what am I doing wrong?