Final answer:
To find the rate of the plane in still air, we can use the concept of relative velocity. Setting up and solving the equation, we find that the rate of the plane in still air is 110 mph.
Step-by-step explanation:
To find the rate of the plane in still air, we can use the concept of relative velocity. Let's assume the rate of the plane in still air is x mph. When the plane is traveling with the wind, the effective rate is increased by the speed of the wind. So, the time it takes to travel 244 mi with the wind can be given by 244/(x+12) hours.
Similarly, when the plane is traveling against the wind, the effective rate is decreased by the speed of the wind. So, the time it takes to travel 196 mi against the wind can be given by 196/(x-12) hours.
Since the time taken in both cases is the same, we can equate the two expressions and solve for x. Setting up the equation:
244/(x+12) = 196/(x-12)
Cross-multiplying,
244(x-12) = 196(x+12)
Simplifying,
244x - 2928 = 196x + 2352
48x = 5280
x = 5280/48 = 110 mph
Therefore, the rate of the plane in still air is 110 mph. Hence, the correct option is a. 180 mph.