Hyperbola story problem

Question

Two LORAN radio stations A and B are 140 kilometers apart and send a simultaneous radio signal to a ship. The signal from B arrives 0.0002 seconds before the signal from A. If the signal travels 300,000 kilometers per second, find the equation of the hyperbola on which the ship is positioned. Use a coordinate system where the origin is the midpoint between the stations, and the stations lie on the x-axis.

Answer 1

Let A located in left focus and B in right; then 2c = 140km; c = 70 km. 2a = 300000·0.0002 km = 60km;

a = 30km; b² = 70² - 30² = 4000. Equation of hyperbola: x²/900 - y²/4000 = 1