Towns A and B are on the equator. A is on longitude 30°W. The time at B is 17:05 when it is 14:05 at A. Find longitude X. A ship sailed east from A to B at 450 knots. Find the travel time.

a) Find the longitude X. Step 1: Calculate the time difference between town B and town A. Time at B = 17:05 hours Time at A = 14:05 hours Time difference = 17:05 - 14:05 = 3 hours. Step 2: Determine the direction of town B relative to town A. Since the time at B is later than the time at A, town B is to the east of town A. Step 3: Convert the time difference into a longitude difference. The Earth rotates 360^ in 24 hours. Therefore, 1 hour corresponds to (360^)/(24) = 15^ of longitude. Longitude difference = 3 hours × 15^/hour = 45^. Step 4: Calculate the longitude of town B (X). Town A is at 30^W. Town B is 45^ to the east of A. Starting from 30^W, moving 30^ east brings us to the Prime Meridian (0^). We need to move an additional 45^ - 30^ = 15^ further east. This means town B is at 15^E. So, X = 15^E. The longitude X is 15^. b) Find the time it took the ship to travel from A to B. Step 1: Calculate the total angular distance between town A and town B. Town A is at 30^W. Town B is at 15^E. The angular distance is the sum of their longitudes because they are on opposite sides of the Prime Meridian. Angular distance = 30^ + 15^ = 45^. Step 2: Convert the angular distance into nautical miles. On the equator, 1^ of longitude corresponds to 60 nautical miles. Distance = 45^ × 60 nautical miles/degree = 2700 nautical miles. Step 3: Calculate the time taken using the formula Time = Distance / Speed. Given speed = 450 knots (450 nautical miles/hour). Time taken = 2700 nautical miles450 nautical miles/hour Time taken = 6 hours. The time it took the ship to travel from A to B is 6 hours.