Final answer:
The submarine traveled for a total of 9 hours before the cruise ship caught up to it, considering the head start and relative speeds of both vehicles.
Step-by-step explanation:
The question involves determining the number of hours a submarine traveled before being caught up to by a cruise ship, given their respective speeds and the head start time of the submarine. To solve this, we use the concept of relative speed and time. Since the submarine has a head start, we first calculate the distance it covers in those three hours, which is 48 miles (16 mph × 3 hours). When the cruise ship starts, it closes the gap at a relative speed of 28 mph - 16 mph = 12 mph.
Let the time taken for the cruise ship to catch up to the submarine be t hours. Then, the distance covered by the cruise ship in that time is 28 mph × t, and the distance covered by the submarine in the same time is 16 mph × t. To close a gap of 48 miles, the distances traveled by both must satisfy the equation: (16 × t) + 48 = 28 × t. Solving for t gives us t = 6 hours. Therefore, the submarine travels for 3 + 6 = 9 hours in total before being caught up to by the cruise ship.