Question

at what rate was the snow falling during the second snowfall?
answer
4 inches every 1 hour
2 inches every 3 hours
3 inches every 2 hours
1 inch every 4 hours

Explanation:

Step1: Identify the time and snow - fall range for the second snowfall

The second snowfall occurs from \(x = 14\) hours to \(x=21\) hours. The snow - on - the - ground values at these times: at \(x = 14\), \(y=7\) inches and at \(x = 21\), \(y = 18\) inches.

Step2: Calculate the rate of change (slope)

The rate of change formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x_1 = 14,y_1=7,x_2 = 21,y_2 = 18\).

$$m=\frac{18 - 7}{21 - 14}=\frac{11}{7}\approx1.57$$

Another way:
The change in snowfall \(\Delta y=18 - 7=11\) inches and the change in time \(\Delta x=21 - 14 = 7\) hours.
If we consider the unit - rate in terms of the given options, we can also use the concept of equivalent ratios.
Let's check each option:

• For the option "4 inches every 1 hour": The slope \(m = 4\) (since \(m=\frac{\Delta y}{\Delta x}\), if \(\Delta y = 4\) and \(\Delta x=1\)).
• For the option "2 inches every 3 hours": \(m=\frac{2}{3}\approx0.67\)
• For the option "3 inches every 2 hours": \(m=\frac{3}{2}=1.5\)
• For the option "1 inch every 4 hours": \(m=\frac{1}{4}=0.25\)

The closest value to our calculated slope (which is \(\frac{11}{7}\approx1.57\)) is \(m = 1.5=\frac{3}{2}\) (3 inches every 2 hours)

Answer:

3 inches every 2 hours