Question

A plane traveled 1104 miles each way to San Francisco and back. The trip there was with the wind. it took 12 hours. The trip back was into the wind. The trip back took 24 hours. what is the speed of the plane in still air? why is the speed of the wind?

Answer 1

The speed of the plane in still air is 69 mph, and the speed of the wind is 23 mph. We found this by setting up equations based on the distances and times given, with the variable x representing the plane's speed and y representing the wind's speed.

Step-by-step explanation:

We need to determine the speed of the plane in still air and the speed of the wind. Since the plane traveled 1104 miles each way with and against the wind, and we know the time it took for each leg of the trip, we can set up two equations to solve for the two unknowns.

Let x be the speed of the plane in still air and y be the speed of the wind. The speed with the wind is x + y and against the wind is x - y.

With the wind (downwind):
x + y = ​​​1104 ​​​miles / 12 hours

Against the wind (upwind):
x - y = ​​​1104 miles / 24 hours

Solving these equations:

1. (x + y) = 92 (since 1104/12 = 92)
2. (x - y) = 46 (since 1104/24 = 46)

Adding both equations, we get:

2x = 138, which means x = 69 mph.

Substituting x back into either equation, we find y = 23 mph.

Therefore, the speed of the plane in still air is 69 mph, and the speed of the wind is 23 mph.