Question

Tanya is training a turtle for a turtle race. For every 1/6 of an hour that the turtle is crawling, he can travel 1/11 of a mile. At what unit rate is the turtle crawling?

Answer 1

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:

\[
\boxed{\frac{6}{11}} \text{ miles per hour}
\]