Final answer:
The rate at which the distance between the two ships is changing can be found using the concept of rate of change. By calculating the derivative of the distance equation, we can find the rate of change at a specific time. In this case, at 4:00 p.m., the rate is approximately 100 * sqrt(13) km/hr.
Step-by-step explanation:
To find the rate at which the distance between the ships is changing, we can use the concept of rate of change. Let's assume that ship A is at the origin (0, 0) and ship B is at the point (0, -170).
Ship A is sailing east at a rate of 30 km/h, which means its position after t hours is (30t, 0). Ship B is sailing north at a rate of 20 km/h, which means its position after t hours is (0, -20t).
Using the distance formula, the distance between the two ships is calculated as:
d = sqrt((30t - 0)^2 + (0 - (-20t))^2)
= sqrt(30^2t^2 + (-20^2t^2))
= sqrt(900t^2 + 400t^2)
= sqrt(1300t^2)
= sqrt(130000t^2)
= 100t * sqrt(13)
To find the rate at which the distance is changing at 4:00 p.m., we need to find the derivative of the above equation with respect to time:
dd/dt = 100 * sqrt(13)
Therefore, the rate at which the distance between the two ships is changing at 4:00 p.m. is approximately 100 * sqrt(13) km/hr.