A Pilot Sets Out from an Airport and Heads in the Direction

A pilot sets out from an airport and heads in the direction N $30 ^ { \circ }$ W, flying at a constant speed of $305$ mi/h. Forty-five minutes later the pilot makes a course and speed correction and now heads in the direction N $50 ^ { \circ }$ W and reduces her speed to $175$ mi/h. Half an hour later, engine trouble forces her to make an emergency landing. Find the distance between the airport and the final landing point

A) $423.8 \mathrm { mi }$
B) $408.8 \mathrm { mi }$
C) $309 \mathrm { mi }$
D) $216.41 \mathrm { mi }$
E) $312.41 \mathrm { mi }$