Question 970320
W+++Start
 ;;;;;;;;+
 ;;;;;;;;;;;;;+SE

The angle between SE and W is 135 degrees.  SE is half way between E (90) and S (180)

Two hours later, the plane flying west has gone 1000 km; the one SE 600 km.  If they were in opposite directions, the distance would be 1600 km; the same direction and it would be 400 km, so the answer is between these values and closer to 1600 km by the picture above.

The angle between them is 135 degrees

The side you want is c.
a=1000
b=600
the angle between is theta, and it is 135 degrees  cos (135)=-(sqrt(2)/2))

C^2=a^2 +b^2-2ab cos theta    LAW OF COSINES

c^2=1000000+360000+2(1000)(600)(.7071) ; .7071 is sqrt (2)/2.  The last term is positive, because the cosine is negative, and there are two negatives.
c^2=1360000+848520=2208520.

c=1486.1 miles.  
This makes intuitive sense.