Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-An airplane flies 480 miles with the wind and 320 against the wind in the same length of time. If the speed of the wind is 20 mph, what is the speed of the airplane in still air?
A) 90 mph
B) 40 mph
C) 100 mph
D) 105 mph

Question

Quizplus · Accepted Answer

Let the speed of the airplane in still air be x mph.
We know that distance traveled = speed x time.
Let's assume the time taken in both cases (with and against the wind) is t hours.
With the wind, the speed of the airplane is (x+20) mph.
Therefore, we can write the equation as:
480 = (x+20) t
Against the wind, the speed of the airplane is (x-20) mph.
Therefore, we can write the equation as:
320 = (x-20) t
We can rearrange these equations to solve for t and equate them to each other since the time taken is the same in both cases:
480/(x+20) = 320/(x-20)
Solving for x, we get x = 100 mph.
Therefore, the speed of the airplane in still air is 100 mph.

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