Final answer:
To find the rate at which the distance between the ships is changing at 4:00 PM, we can use the Pythagorean theorem and the derivative.
Step-by-step explanation:
To find how fast the distance between the ships is changing, we can use the Pythagorean theorem. Let's call the distance between the ships D. At any given time, ship A has traveled 20t km, where t represents the number of hours after noon. Ship B has traveled 15t km. Using the Pythagorean theorem, we can set up the equation: D^2 = (110 + 20t)^2 + (15t)^2. Now, we can take the derivative of both sides with respect to time d(D^2)/dt = 2(110 + 20t)(20) + 2(15t)(15) and evaluate it at 4:00 PM.