Question

Flying with the wind a plane went 245 flying into the Dane wind the plane only went 205 mph find the speed of the wind and the speed of the plane in still air

Answer 1

Let's denote the speed of the plane in still air as \( p \) (in mph) and the speed of the wind as \( w \) (in mph).

When the plane is flying with the wind, its effective speed is the sum of its speed and the wind's speed:
\[
p + w = 245
\]

When the plane is flying against the wind, its effective speed is the difference between its speed and the wind's speed:
\[
p - w = 205
\]

Now, we have a system of two equations:

1. \( p + w = 245 \) (1)
2. \( p - w = 205 \) (2)

To solve this system, we can add the two equations together:

\[
(p + w) + (p - w) = 245 + 205
\]

This simplifies to:

\[
2p = 450
\]

Now, divide both sides by 2:

\[
p = 225
\]

Now that we have the speed of the plane in still air, we can substitute \( p \) back into one of the original equations to find the speed of the wind. We'll use equation (1):

\[
225 + w = 245
\]

Subtract 225 from both sides:

\[
w = 20
\]

Now we have both speeds:

- The speed of the plane in still air is \( \mathbf{225} \, \text{mph} \).
- The speed of the wind is \( \mathbf{20} \, \text{mph} \).