If a plane can travel 470 miles per hour with the wind and 390 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air.
Let x be the speed of the plane in still air and y be the speed of the wind.
With the wind, the speed of the plane is x + y.
Against the wind, the sped of the plane is x - y.
According to the problem, we have the following equations:
x + y = 470
x - y = 390
Solving these two equations, we can find the values of x and y.
Adding the two equations, we get 2x = 860
Dividing both sides by 2, we get x = 430.
Substituting the value of x into either equation, we get 430 + y = 470
Subtracting 430 from both sides, we get y = 40.
Therefore, the speed of the plane in still air is 430 mph and the speed of the wind is 40 mph.