Question 203559
They set off at 1pm and we are looking at how far apart they are at 3pm - ie 2 hours later.

In two hours, the first plane will have gone due north a distance of 2 X 150 = 300 miles.

The second plane will have gone due west a distance of 2 X 200 = 400 miles.

We now have a nice right angle triangle in which the length of one side is 300 and the length of the other side is 400 - And we are looking for the distance across the hypotenuse.

Pythagoras helps us out here.  The square of the distance between the planes = 300^2 + 400^2

Actually, this forms a neat pythagorean triangle - the distance between the planes is 500 miles.