An airplane flying against the wind travels 100 miles in the same amount of time it would take the same plane to travel 140 miles with the wind. If the wind speed is a constant 40 miles per hour, how fast would the plane travel in still air?
100/(p-40) = 140/(p+40)
p = 240
To find the speed of the plane in still air, we need to set up an equation using the given information. Let's denote the speed of the plane as "x" (in miles per hour).
When the plane is flying against the wind, its effective speed decreases by the speed of the wind. So, the plane's speed against the wind would be (x - 40) mph.
Similarly, when the plane is flying with the wind, its effective speed increases by the speed of the wind. So, the plane's speed with the wind would be (x + 40) mph.
We are told that the plane takes the same amount of time to travel 100 miles against the wind as it does to travel 140 miles with the wind. Since speed is equal to distance divided by time, we can set up the following equation:
100 / (x - 40) = 140 / (x + 40)
To solve this equation, we can cross-multiply:
100(x + 40) = 140(x - 40)
Expanding the equation:
100x + 4000 = 140x - 5600
Rearranging to isolate the x terms:
100x - 140x = -5600 - 4000
-40x = -9600
Dividing both sides by -40:
x = -9600 / -40
Simplifying, we get:
x = 240
Therefore, the speed of the plane in still air is 240 miles per hour.