Question

snow fell for 9 hours at a rate of \(\frac{1}{2}\) inch per hour. Before the snowstorm began, there were already 6 inches of snow on the ground. The equation \(y=\frac{1}{2} x+6\) models the depth \(y\) of snow on the ground after \(x\) hours. Writing In the Apple County School District, school is canceled if there is a foot or more of snow on the ground. If this 9-hour storm occurred in Apple County, would school be canceled? Explain your reasoning.

Short answer

No, school would not be canceled in Apple County. The total snowfall of 10.5 inches after the 9-hour storm is less than a foot, so it does not meet the district's cancellation conditions.

Step-by-step solution

Understanding of Problem and Equation

The equation \(y=\frac{1}{2}x+6\) represents the total depth of the snow. Here, \(x\) represents the number of hours the snowfall lasts and \(\frac{1}{2}x\) is the amount of snow that falls each hour. The \(+6\) represents the snow that was already on the ground before the snowstorm started.

Substituting Given Values

Now, by substituting the given value of \(x=9\) hours into the equation, we find the total snow depth. So, \( y = \frac{1}{2} * 9 + 6 \)

Calculating Total Snow Depth

Carrying out the calculation, \( y = 4.5 + 6 = 10.5 \) inches.

Comparing With the Cancellation Condition

Apple county cancels school if there is a foot or more of snow. A foot is equivalent to 12 inches. So, comparing 10.5 inches with 12 inches, the snowfall is less than a foot.

Making Conclusion

Since the total snowfall, 10.5 inches, is less than 12 inches (a foot), according to the rules of the Apple County School District, school would not be canceled.