Question

5. Two LORAN (long range navigation) stations A and B are situated along
a straight shore, where A is 200 miles west of B. These stations transmit
radio signals at a speed 186 miles per millisecond. The captain of a ship
travelling on the open sea intends to enter a harbor that is located 40 miles
east of station A. Due to the its location, the harbor experiences a time
difference in receiving the signals from both stations. The captain
navigates the ship into the harbor by following a path where the ship
experiences the same time difference as the harbor.
a. What time difference between station signals should the captain be
looking for in order the ship to make a successful entry into the
harbor?
b. If the desired time difference is achieved, determine the location of
the ship if it is 75 miles offshore.​

Answer 1

Given:

A is 200 miles west of B

radio signals at a speed 186 miles per millisecond

harbor that is located 40 miles  east of station A

(a) The captain be looking for in order to ship to make a successful entry  into the harbor

$=\frac{200}{40} - \frac{200}{186}$

=5 - 1.075

=3.925

(b) The desire time different is achieved ship it is 75 miles offshore

$=\frac{75}{40}$

=1.875

Hence the answer is 1.875