Question

An airplane flew with the wind for 1 hour and returned the same distance against the wind in 134 hours. If the speed of the wind was 30 mph, what was the speed of the plane in still air?​

Answer 1

To find the speed of the plane in still air, given the speed of the wind, we used the equation (p + 30) = (p - 30) * 1.34, resulting in a speed of approximately 206.47 mph for the plane in still air.

Step-by-step explanation:

The student has asked a question about determining the speed of an airplane in still air, given its performance with and against the wind. To solve this, let's denote the speed of the plane in still air as 'p' and the speed of the wind as 'w'. Since 'w' is given as 30 mph, when the plane flies with the wind, its ground speed is (p + w), and against the wind, its ground speed is (p - w).

We know the plane flew for 1 hour with the wind and 1.34 hours against it, covering the same distance. Thus, we have two equations:

1. (p + 30) * 1 = Distance
2. (p - 30) * 1.34 = Distance

Since the distances are equal:

(p + 30) = (p - 30) * 1.34

Now let's solve for 'p':

p + 30 = 1.34p - 40.2

0.34p = 70.2

p = 70.2 / 0.34

p ≈ 206.47 mph

Therefore, the speed of the plane in still air is approximately 206.47 mph.