Question

Beginning 145 miles directly south of the city of Hartville, a car travels due west. If the car is travelling at a speed of 42 miles per hour, determine the rate of change of the distance between Hartville and the car when the car has been travelling for 55 miles. (Do not include units in your answer, and round to the nearest hundredth.)

Answer 1

The rate of change of the distance between Hartville and the car when the car has been traveling for 55 miles is 152.67 miles per hour.

Step-by-step explanation:

To determine the rate of change of the distance between Hartville and the car, we can use the concept of average speed. The average speed is calculated by dividing the total distance traveled by the total time taken. In this case, the car travels for 55 miles due west. The total distance traveled by the car is 145 + 55 = 200 miles. The total time taken is given by dividing the distance traveled by the speed, which is 55 miles / 42 miles per hour = 1.31 hours. Therefore, the average speed is 200 miles / 1.31 hours = 152.67 miles per hour.