A ship is sailing due north at 24 mph toward a coastal battery with a maximum range of 5 nautical miles. How long will the ship be in range of the battery if it approaches within 4 nautical miles?

To determine how long the ship will be in range of the coastal battery, we need to first calculate how far the ship will travel to come within 4 nautical miles of the battery.

The ship is currently 5 nautical miles away from the battery and is approaching at a speed of 24 mph. To convert this speed into nautical miles per minute, we note that 1 nautical mile is approximately equal to 1.15 statute miles. Thus, 24 mph can be expressed in nautical miles per minute by dividing it by 60 to get the speed in miles per minute, then converting statute miles to nautical miles.

1. Convert 24 mph to nautical miles per minute:

   • 24 statute miles per hour = 24 / 60 = 0.4 statute miles per minute.
   • 0.4 statute miles per minute / 1.15 = approximately 0.348 nautical miles per minute.

2. The ship must cover a distance from 5 nautical miles to 4 nautical miles, which is 1 nautical mile.

3. To find the time taken to cover that distance, we divide the distance by the speed:

   • Time = Distance / Speed = 1 nautical mile / 0.348