Question

A plane flies between two cities that are 1120 miles apart. When going with the wind, the plane makes the journey in (7)/(2) hour (s). When going against the wind, it takes 4 hour (s)

Answer 1

To find the speed of the plane in still air and the speed of the wind, we can set up a system of equations using the given information. Solving the equations will give us the required values.

Step-by-step explanation:

To solve this problem, we can use the formula Speed = Distance / Time. Let's call the speed of the plane in still air S and the speed of the wind W. When the plane is flying with the wind, the effective speed is S + W, and when it's flying against the wind, the effective speed is S - W.

Given that the plane takes (7)/(2) hours to travel 1120 miles with the wind, we can set up the equation:

S + W = 1120 / (7/2) = 320 mph

Similarly, when the plane is flying against the wind, it takes 4 hours:

S - W = 1120 / 4 = 280 mph

Now, we can solve these two equations to find the values of S and W. Adding the two equations together, we get:

2S = 600

S = 300

Substituting the value of S back into one of the original equations, we can find the value of W:

300 + W = 320

W = 20

So, the speed of the plane in still air is 300 mph, and the speed of the wind is 20 mph.