Question

A plane traveled 550 mph with the wind and 410 against the wind. Find the speed of the plane in still air and the speed of the wind. (Assume the plane flies the same distance in both directions)

a) Plane speed = 480 mph, Wind speed = 70 mph
b) Plane speed = 480 mph, Wind speed = 60 mph
c) Plane speed = 480 mph, Wind speed = 50 mph
d) Plane speed = 480 mph, Wind speed = 40 mph

Answer 1

The speed of the plane in still air is 480 mph, and the speed of the wind is 70 mph.

Step-by-step explanation:

Let's assume the speed of the plane in still air is x mph and the speed of the wind is y mph.

When flying with the wind, the speed of the plane is x + y mph. Therefore, we can write the equation:

x + y = 550

When flying against the wind, the speed of the plane is x - y mph. Therefore, we can write the equation:

x - y = 410

Solving these two equations simultaneously, we can find the values of x and y.

Adding the two equations: (x + y) + (x - y) = 550 + 410
2x = 960
x = 480

Substituting the value of x into one of the original equations, we can find the value of y.

480 - y = 410
y = 70

Therefore, the speed of the plane in still air is 480 mph, and the speed of the wind is 70 mph. So the correct answer is (a) Plane speed = 480 mph, Wind speed = 70 mph.