Question

Two cars start moving from the same point. One travels south at 24mi/h and the other travels west at 18mi/h. At what rate is the distance between the cars increasing two hours later?

Answer 1

The rate at which the distance between the cars is increasing two hours later is 60 miles per hour.

Step-by-step explanation:

To find the rate at which the distance between the cars is increasing, we can use the concept of relative velocity. Since one car is traveling south and the other is traveling west, they are moving in perpendicular directions. We can use the Pythagorean theorem to find the total distance between the cars at any given time.

After two hours, the first car has traveled a distance of 24 mph * 2 hours = 48 miles south, and the second car has traveled a distance of 18 mph * 2 hours = 36 miles west.

Using the Pythagorean theorem, the distance between the cars is sqrt((48 miles)^2 + (36 miles)^2) = 60 miles. Therefore, the rate at which the distance between the cars is increasing two hours later is 60 miles per hour.