A Plane Leaves the Airport at 4:00 P $10 ^ { \circ }$

Multiple Choice

A plane leaves the airport at 4:00 p.m. and heads in the direction N $10 ^ { \circ }$ E at a constant speed of $250$ mi/h. Forty-five minutes later, a jet leaves the same airport and flies N $60 ^ { \circ }$ W at a constant speed of $450$ mi/h. Find the distance between the plane and the jet at 5:30 p.m

A) $409.8 \mathrm { mi }$
B) $904.8 \mathrm { mi }$
C) $309 \mathrm { mi }$
D) $7.5 \mathrm { mi }$
E) $77 \mathrm { mi }$