If a plane can travel 400 miles per hour with the wind and 400 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air.
What is the speed of the wind? mph
Let's assume the speed of the plane in still air is x mph and the speed of the wind is y mph.
When the plane is flying with the wind, its effective speed is increased by the speed of the wind. So, the speed of the plane with the wind is x+y mph.
Similarly, when the plane is flying against the wind, its effective speed is decreased by the speed of the wind. So, the speed of the plane against the wind is x-y mph.
Given that the speed of the plane with the wind is 400 mph and the speed of the plane against the wind is also 400 mph.
So, we have the system of equations:
x + y = 400 ...(1)
x - y = 400 ...(2)
Adding equations (1) and (2), we get:
2x = 800
Dividing both sides by 2, we get:
x = 400
Substituting the value of x in equation (1), we get:
400 + y = 400
y = 0
Therefore, the speed of the wind is 0 mph.
sorry its 460 miles per hour with wind and 400 per hour agianst the wind
No problem. Let's solve the problem with the corrected values.
Assuming the speed of the plane in still air is x mph and the speed of the wind is y mph, we have the following equations:
x + y = 460 ...(1) (plane's speed with the wind)
x - y = 400 ...(2) (plane's speed against the wind)
To find the speed of the wind, we can add equations (1) and (2):
(x + y) + (x - y) = 460 + 400
2x = 860
x = 430
Now we can substitute the value of x into equation (1) or (2):
430 + y = 460
y = 460 - 430
y = 30
Therefore, the speed of the wind is 30 mph.