Flying with the wind a plane went 162 mph. Flying into the same wind the plane only went 82mph. Find the speed of the plane in still air and the speed of the wind.
the still-air speed is the average of the other two speeds, since the same amount is added or subtracted to get the final air speeds.
To find the speed of the plane in still air and the speed of the wind, we can set up a system of equations.
Let's assume that the speed of the plane in still air is x mph, and the speed of the wind is y mph.
When flying with the wind, the plane's speed is increased by the speed of the wind. Therefore, the plane's speed can be expressed as (x + y) mph.
When flying against the wind, the wind's speed reduces the plane's speed. Therefore, the plane's speed can be expressed as (x - y) mph.
Given that when flying with the wind, the plane's speed is 162 mph, we can write the equation:
(x + y) = 162
Similarly, when flying against the wind, the plane's speed is 82 mph, leading to the equation:
(x - y) = 82
Now we have a system of equations:
(x + y) = 162
(x - y) = 82
To solve this system, we can use the method of elimination. Adding the two equations together eliminates the variable y:
(x + y) + (x - y) = 162 + 82
2x = 244
x = 122
The speed of the plane in still air (x) is 122 mph.
Substituting the value of x back into either equation, we can solve for y:
(122 + y) = 162
y = 162 - 122
y = 40
The speed of the wind (y) is 40 mph.
Therefore, the speed of the plane in still air is 122 mph, and the speed of the wind is 40 mph.