In the LORAN (LOng RAnge Navigation) Radio Navigation System, Two $$| A | - | B |$$

Multiple Choice

In the LORAN (LOng RAnge Navigation) radio navigation system, two radio stations located at A and B transmit simultaneous signals to a ship or an aircraft located at P. The onboard computer converts the time difference in receiving these signals into a distance difference $$| A | - | B |$$ , and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure) . Suppose that station B is located L = $$440$$ mi due east of station A on a coastline. A ship received the signal from B $1280$ microseconds (µs) before it received the signal from A. Assuming that radio signals travel at a speed of $980$ ft /µs and if the ship is due north of B, how far off the coastline is the ship? Round your answer to the nearest mile.

A) $287$ miles
B) $291$ miles
C) $288$ miles
D) $289$ miles
E) $290$ miles