Question

an airplane can travel 550 mph in still air. if it travels 3498 miles with the wind in the same length of time it travels 3102 miles against the wind, what is the speed of the wind?

Answer 1

The speed of the wind is approximately 56.8 mph.

Step-by-step explanation:

To find the speed of the wind, we can set up two equations based on the given information. Let's assign a variable to the speed of the wind, let's say w:

Plane's speed with the wind = Plane's speed in still air + Speed of the wind

Plane's speed against the wind = Plane's speed in still air - Speed of the wind

Substituting given values into the equations, we get:

550 + w = 3498/t

550 - w = 3102/t

Next, we can solve this system of equations to find the value of w, the speed of the wind.

First, we can solve the second equation for t:

t = 3102/(550 - w)

Substituting this expression for t into the first equation, we get:

550 + w = 3498/(3102/(550 - w))

Simplifying this equation, we get:

w = 625/11

So, the speed of the wind is approximately 56.8 mph.

Answer 2

The 20 mph headwind slows the plane down. This is because the headwind comes at the head of the plane and goes in the opposite direction of the plane.

So the plane's actual speed (with the wind included) is 550-20 = 530 mph.