__The Question:__In the

**LORAN**(

**Lo**ng

**Ra**nge

**N**avigation) radio navigation system, two radio stations located at A and B transmit simultaneous signals to a ship located at P. The onboard computer converts the time difference in receiving these signals into a distance difference |PA| - |PB|, and this, according to the definition of a hyperbola, locates the ship on one branch of a hyperbola (

**see the figure).**Suppose that station B is located 400 mi due east of station A on a coastline. A ship received the signal from B 1200 microseconds (ms) before it received the signal from A.

(a) Assuming that radio signals travel at a speed of 980 ft/ms, find an equation of the hyperbola on which the ship lies.

__The Solutions__(b) If the ship is due north of B, how far of the coastline is the ship?