an airplane flying with the wind can cover 660 miles in 2 hours. The return trip against the wind takes 2 1/2 hours.
complete the question.
To solve this problem, we can use the formula:
Distance = (Speed + Wind speed) × Time
Let's consider the variables:
Let "S" be the speed of the airplane in still air (without wind).
Let "W" be the speed of the wind.
Given that the airplane can cover 660 miles in 2 hours flying with the wind, we can write the equation as:
660 = (S + W) × 2
Similarly, for the return trip against the wind, the equation becomes:
660 = (S - W) × 2.5
Now we have a system of equations that we can solve simultaneously to find the values of S and W.
Equation 1: 660 = (S + W) × 2
Divide both sides by 2:
330 = S + W
Equation 2: 660 = (S - W) × 2.5
Divide both sides by 2.5:
264 = S - W
Now we have a system of equations:
330 = S + W
264 = S - W
To solve this system of equations, we can add the equations together to eliminate "W":
330 + 264 = S + W + S - W
594 = 2S
Divide both sides by 2:
S = 297
Now that we know S, we can substitute it back into either of the original equations to find W.
Using Equation 1:
330 = S + W
330 = 297 + W
W = 33
So, the speed of the airplane in still air (without wind) is 297 mph, and the speed of the wind is 33 mph.