Two radio stations are located 180 miles apart along a coast. If a ship records a time difference of 0.0006 second and continues on the hyperbolic path corresponding to that difference, where will it reach shore? Round to the nearest mile. (Assume the speed of the radio signal is 186,000 miles per second.)
A) The ship reaches shore between the two stations, 68 miles from one station and 292 miles from the other.
B) The ship reaches shore between the two stations, 34 miles from one station and 146 miles from the other.
C) The ship reaches shore between the two stations, 124 miles from one station and 236 miles from the other.
D) The ship reaches shore between the two stations, 152 miles from one station and 208 miles from the other.

Question

Quizplus · Accepted Answer

The time difference of 0.0006 seconds corresponds to a distance difference of 111.6 miles (0.0006 * 186,000). The hyperbola's foci are the two stations, and the ship is on a hyperbolic path where the difference in distances to the two stations is 111.6 miles. Solving for the point on the hyperbola closest to the shore gives the distances as 34 miles and 146 miles from the two stations.

Two Radio Stations Are Located 180 Miles Apart Along a Coast