Question

An airplane travels 3415 kilometers against the wind in 5 hours and 4065 kilometers with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?

A. The rate of the plane in still air is 680 km/h, and the rate of the wind is 45 km/h.
B. The rate of the plane in still air is 725 km/h, and the rate of the wind is 30 km/h.
C. The rate of the plane in still air is 645 km/h, and the rate of the wind is 40 km/h.
D. The rate of the plane in still air is 700 km/h, and the rate of the wind is 55 km/h.

Answer 1

By using a system of equations, we find that the rate of the plane in still air is 748 km/h and the rate of the wind is 65 km/h.

Step-by-step explanation:

To find the rate of the plane in still air and the rate of the wind, we can set up a system of equations based on the information given:

• The plane travels 3415 kilometers against the wind in 5 hours.
• The plane travels 4065 kilometers with the wind in the same amount of time (5 hours).

Let's denote the rate of the plane in still air as P and the rate of the wind as W.

Against the wind, the plane's effective speed is P - W, and with the wind, the plane's effective speed is P + W.

Now we can set up our equations:

1. 3415 km = 5 hours * (P - W)
2. 4065 km = 5 hours * (P + W)

Dividing both sides of the equations by 5 yields:

1. 683 km/h = P - W
2. 813 km/h = P + W

By adding the two equations, we can find the rate of the plane in still air (P):

683 km/h + 813 km/h = 2P

1496 km/h = 2P

P = 748 km/h

We substitute P in one of the equations to find W:

683 km/h = 748 km/h - W

W = 748 km/h - 683 km/h

W = 65 km/h

Thus, the rate of the plane in still air is 748 km/h, and the rate of the wind is 65 km/h.