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. 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.

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