Three LORAN radio transmitters, A, B, and C, are located 200 miles apart along a straight coastline. They simultaneously transmit radio signals at regular intervals. The signals travel at a speed of 980 feet per microsecond. A ship, at S, first receives a signal from transmitter B. After 264 microseconds, the ship receives the signal from transmitter C, and then another 264 microseconds later it receives the signal from transmitter A. Use the diagram at right to answer these questions to find the location of the ship.

a. Find d2 - d1. Express your answer in miles (1 mi = 5280 ft).
b. Find d3 - d1. Express your answer in miles.
c. Use the fact that d2 - d1 is constant to write the equation of the hyperbola represented in 10a. Note that transmitters B and C are located at the foci.
d. Write the equation of the hyperbola represented in 10b.
e. Graph the hyperbolas and find the coordinates of the location of the ship. How can you be sure which of the intersection points represents the ship?

ds di lou 3