Question

Car A and Car B both start from the same position. Car A travels north at 30mph and Car B travels west at 20mph. Find the rate at which the distance between the two cars is changing at time t = 2 hours.

Answer 1

about 36.1 miles per hour

Explanation:

The cars' distance from the starting point is proportional to time, since both started at the same time. 1 hour after they started, Car A is 30 miles north of the origin, and Car B is 20 miles west of the origin. The distance between them can be found using the Pythagorean theorem:

d = √(30² +20²) = √(900 +400) = 10√13 ≈ 36.056

The distance between the cars is increasing at the constant rate of about 36.1 miles per hour.