Question

1. it takes santa 5 minutes to fly 35 miles with the wind. it takes him 7 minutes to go 35 miles against the wind. determine the speed of santa’s sleigh in still air (x) and the speed of the wind (y).

ordered pair m: ______

Explanation:

Step1: Convert time to hours

5 minutes = $\frac{5}{60}=\frac{1}{12}$ hours, 7 minutes = $\frac{7}{60}$ hours.

Step2: Set up speed equations

With wind: speed = $x + y=\frac{35}{\frac{1}{12}} = 420$ mph.
Against wind: speed = $x - y=\frac{35}{\frac{7}{60}} = 300$ mph.

Step3: Solve the system of equations

We have

$$\begin{cases}x + y = 420\\x - y = 300\end{cases}$$

.
Add the two equations: $2x = 720\Rightarrow x = 360$.
Substitute $x = 360$ into $x + y = 420$: $360 + y = 420\Rightarrow y = 60$.

Answer:

The speed of Santa’s sleigh in still air is 360 mph and the speed of the wind is 60 mph. The ordered pair (x, y) is (360, 60).