Question

"Flying to Chicago with a tailwind, a plane averaged 300 km/h. On the return trip, the plane only averaged 278 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air."

Answer 1

The speed of the plane in still air is 289 km/h, and the speed of the wind is 11 km/h. This was determined by setting up a system of equations using the given average speeds with and against the wind, and solving for the plane's speed in still air and the wind speed.

Step-by-step explanation:

To solve the problem of determining the speed of the wind and the speed of the plane in still air, when given the plane's average speeds with and against the wind, we set up a system of equations based on the relationship between the wind speed, plane speed in still air, and ground speed.

Let p represent the speed of the plane in still air and w represent the speed of the wind. When the plane flies with a tailwind, its ground speed is p + w, and when it flies into a headwind, its ground speed is p - w. From the question we have two equations:

1. p + w = 300 km/h (speed with tailwind)
2. p - w = 278 km/h (speed against the wind)

Adding these two equations together helps to eliminate the wind variable w:

p + w + p - w = 300 + 278

2p = 578

p = 289 km/h (plane's speed in still air)

To find the speed of the wind, we can substitute the value of p into one of the original equations:

289 + w = 300

w = 300 - 289

w = 11 km/h (speed of the wind)

The plane's speed in still air is 289 km/h and the speed of the wind is 11 km/h.