A plane begins its takeoff at 2:00 P.M. on a 3400-mile flight. After 7.5 hours, the plane arrives at its destination. Explain why there are at least two times during the flight when the speed of the plane is 400 miles per hour.
A) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 716 mi/hr. The speed was 400 mi/hr when the plane was accelerating to 716 mi/hr and decelerating from 716 mi/hr.
B) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 358 mi/hr. The speed was 400 mi/hr when the plane was accelerating to 358 mi/hr and decelerating from 358 mi/hr.
C) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 227 mi/hr. The speed was 400 mi/hr when the plane was accelerating to 227 mi/hr and decelerating from 227 mi/hr.
D) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 302 mi/hr. The speed was 400 mi/hr when the plane was accelerating to 302 mi/hr and decelerating from 302 mi/hr.
E) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 453 mi/hr. The speed was 400 mi/hr when the plane was accelerating to 453 mi/hr and decelerating from 453 mi/hr.

Question

A plane begins its takeoff at 2:00 P.M. on a 3400-mile flight. After 7.5 hours, the plane arrives at its destination. Explain why there are at least two times during the flight when the speed of the plane is 400 miles per hour. ​
A) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 716 mi/hr. The speed was 400 mi/hr when the plane was accelerating to 716 mi/hr and decelerating from 716 mi/hr.
B) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 358 mi/hr. The speed was 400 mi/hr when the plane was accelerating to 358 mi/hr and decelerating from 358 mi/hr.
C) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 227 mi/hr. The speed was 400 mi/hr when the plane was accelerating to 227 mi/hr and decelerating from 227 mi/hr.
D) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 302 mi/hr. The speed was 400 mi/hr when the plane was accelerating to 302 mi/hr and decelerating from 302 mi/hr.
E) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 453 mi/hr. The speed was 400 mi/hr when the plane was accelerating to 453 mi/hr and decelerating from 453 mi/hr.

Quizplus · Accepted Answer

The average speed of the plane is calculated by dividing the total distance by the total time of the flight. For a 3400-mile flight that takes 7.5 hours, the average speed is $ \frac{3400 \text{ miles}}{7.5 \text{ hours}} = 453.33 \text{ miles per hour} $. The Mean Value Theorem suggests that at some point(s) during the flight, the plane must travel at its average speed. However, the explanation that there must be at least two times the plane's speed is exactly 400 miles per hour is not directly related to the Mean Value Theorem but rather to the practical aspects of a plane's speed changes (acceleration and deceleration) around this average speed.

A Plane Begins Its Takeoff at 2:00 P