Final answer:
To find the rate at which the distance between Car A and Car B is changing, we use the Pythagorean theorem and differentiate with respect to time, applying the given speeds of the cars. This related rates calculus problem yields the speed at which the two cars are moving apart.
Step-by-step explanation:
The question involves calculating the rate at which the distance between two cars is changing. This is a classic problem of related rates in calculus. To solve the problem, consider the position of each car relative to the intersection point P. We can create a right triangle where the horizontal leg represents the eastward distance of car B from P, and the vertical leg represents the northward distance of car A from P. The hypotenuse of this triangle will represent the distance between the two cars.
To find the rate at which the distance between the two cars is changing, we will use the Pythagorean theorem to relate the distances and their rates of change, and then differentiate with respect to time. Since Car A's distance from point P is changing at 80 km/hr and Car B's is changing at 115 km/hr, the derivative of the hypotenuse with respect to time will give us the rate at which the distance between the two cars is changing. By applying the chain rule and substituting the given rates, we can find this derivative, which represents the speed at which the cars are moving apart.