Question

A plane flies from Oahu and back. Flying to Oahu the plane is flying against the wind and the trip takes 6 hours. On the way back the plane flies with the wind and it takes 5 hours. If the distance one way is 900 miles, what is the speed of the plane in still air and the speed of the wind?

Answer 1

Plane: 165 miles per hour

Wind: 15 miles per hour

Step-by-step explanation:

Let's call x the speed of the plane in still air and y the speed of the wind.

Additionally, the velocity is equal to distances over time. So, when the plane is flying against the wind, we can write the following equation:

`\begin{gathered} x-y=\frac{\text{distance}}{\text{time}} \\ x-y=\frac{900\text{ miles}}{6\text{ hours}} \\ x-y=150 \end{gathered}`

Because x - y is the total velocity of the plane when it is flying against the wind.

On the other hand, when the plane flies with the wind, we get:

`\begin{gathered} x+y=\frac{900\text{ miles}}{5\text{ hours}} \\ x+y=180 \end{gathered}`

So, we have the following system of equations:

x - y = 150

x + y = 180

Adding both equations, we get:

x - y = 150

x + y = 180

2x + 0 = 330

Solving for x:

2x = 330

2x/2 = 330/2

x = 165

Finally, Replace x by 165 on the second equation and solve for y as:

x + y = 180

165 + y = 180

165 + y - 165 = 180 - 165

y = 15

Therefore, the speed of the plane in still air is 165 miles per hour and the speed of the air is 15 miles per hour.