To determine the unit rate at which the turtle is crawling, we need to find out how far the turtle travels in one hour.
We know that:
- In \( \frac{1}{6} \) of an hour, the turtle travels \( \frac{1}{11} \) of a mile.
To find out how far the turtle travels in one hour, we can set up a proportion. If the turtle travels \( \frac{1}{11} \) of a mile in \( \frac{1}{6} \) of an hour, then in 1 hour, the turtle would travel:
\[ \text{Distance in 1 hour} = \left( \text{Distance in } \frac{1}{6} \text{ hour} \right) \times \left( \text{Number of } \frac{1}{6} \text{ hours in 1 hour} \right) \]
The number of \( \frac{1}{6} \) hours in 1 hour can be calculated as:
\[ 1 \text{ hour} \div \frac{1}{6} \text{ hour} = 1 \times \frac{6}{1} = 6 \]
Thus, in 1 hour, the turtle will travel:
\[ \text{Distance in 1 hour} = \frac{1}{11} \text{ miles} \times 6 = \frac{6}{11} \text{ miles} \]
Now we have the unit rate of the turtle's crawling speed, which is:
\[ \frac{6}{11} \text{ miles per hour} \]
Thus, the unit rate at which the turtle is crawling is:
\[ \boxed{\frac{6}{11}} \text{ miles per hour} \]