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

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 $\mathrm { L } = 480 \mathrm { mi }$ due east of station $A$ on a coastline. $\mathrm { A }$ ship received the signal from $B 1280$ microseconds $( \mu s )$ before it received the signal from $A$ .
Assuming that radio signals travel at a speed of $1000 \mathrm { ft } / \mu \mathrm { s }$ and if the ship is due north of $B$ , how far off the coastline is the ship? Round your answer to the nearest mile. Select the correct answer.

A) 355 miles
B) 358 miles
C) 357 miles
D) 354 miles
E) 356 miles