Carol is cross-country skiing. The table shows the distance she traveled after various numbers of minutes. What is the rate of change?

To find the rate of change of the distance Carol traveled while cross-country skiing, we need to look at the change in distance traveled over the change in time. This can be expressed as:

\[
\text{Rate of Change} = \frac{\text{Change in Distance}}{\text{Change in Time}} = \frac{\Delta d}{\Delta t}
\]

From the data provided, we will first calculate the distance traveled at each key point in time (in minutes):

- At 2 minutes: \(\frac{1}{6}\) miles
- At 3 minutes: \(\frac{17}{48}\) miles
- At 4 minutes: \(\frac{13}{24}\) miles
- At 5 minutes: \(\frac{35}{48}\) miles
- At 6 minutes: \(\frac{11}{12}\) miles

Next, let's analyze the change in distance traveled between each pair of consecutive time intervals.

1. **From 2 to 3 minutes**:
\[
\text{Change in Distance} = \frac{17}{48} - \frac{1}{6} = \frac{17}{48} - \frac{8}{48} = \frac{9}{48} = \frac{3}{16}
\]
\[
\text{Change in Time} = 3 - 2 = 1 \text{ minute}
\]
\[
\text{Rate of Change} = \frac{\frac{3}{16}}{1} = \frac{3}{16} \text{ miles per minute}
\]

2. **From 3 to 4 minutes**:
\[
\text{Change in Distance} = \frac{13}{24} - \frac{17}{48}
\]
First, convert \(\frac{13}{24}\) to a common denominator of 48:
\[
\frac{13}{24} = \frac{26}{48}
\]
Now calculate the change:
\[
\text{Change in Distance} = \frac{26}{48} - \frac{17}{48} = \frac{9}{48} = \frac{3}{16}
\]
\[
\text{Change in Time} = 4 - 3 = 1 \text{ minute}
\]
\[
\text{Rate of Change} = \frac{\frac{3}{16}}{1} = \frac{3}{16} \text{ miles per minute}
\]

3. **From 4 to 5 minutes**:
\[
\text{Change in Distance} = \frac{35}{48} - \frac{13}{24}
\]
Convert \(\frac{13}{24}\) again:
\[
\text{Change in Distance} = \frac{35}{48} - \frac{26}{48} = \frac{9}{48} = \frac{3}{16}
\]
\[
\text{Change in Time} = 5 - 4 = 1 \text{ minute}
\]
\[
\text{Rate of Change} = \frac{\frac{3}{16}}{1} = \frac{3}{16} \text{ miles per minute}
\]

4. **From 5 to 6 minutes**:
\[
\text{Change in Distance} = \frac{11}{12} - \frac{35}{48}
\]
Convert \(\frac{11}{12}\) to a common denominator of 48:
\[
\frac{11}{12} = \frac{44}{48}
\]
Now calculate:
\[
\text{Change in Distance} = \frac{44}{48} - \frac{35}{48} = \frac{9}{48} = \frac{3}{16}
\]
\[
\text{Change in Time} = 6 - 5 = 1 \text{ minute}
\]
\[
\text{Rate of Change} = \frac{\frac{3}{16}}{1} = \frac{3}{16} \text{ miles per minute}
\]

In summary, the rate of change of the distance Carol traveled while cross-country skiing is consistently:

\[
\frac{3}{16} \text{ miles per minute}
\]