Question

Two cars are moving from the same point. One travels North 20 mi/h and the other trsvels east at 25mi/hr. At what rate is the distance between the cars increasing two hours later?

Answer 1

After two hours, the distance between the two cars is increasing at a rate of sqrt(1025) mi/h.

Step-by-step explanation:

To determine the rate at which the distance between the two cars is increasing, we can use the Pythagorean theorem. Let's consider the position of the cars after two hours. Car A has been traveling north at a speed of 20 mi/h, which means it has traveled a distance of 20 mi. Car B has been traveling east at a speed of 25 mi/h, which means it has traveled a distance of 25 mi.

Using the Pythagorean theorem, we can find the distance between the two cars after two hours:

Distance^2 = (20 mi)^2 + (25 mi)^2

Distance^2 = 400 mi^2 + 625 mi^2

Distance^2 = 1025 mi^2

Distance = sqrt(1025) mi

Therefore, after two hours, the distance between the two cars is increasing at a rate of sqrt(1025) mi/h.