Question

Tanya is training a turtle for a turtle race. For every 5/6 of an hour that the turtle is crawling, he can travel 3/20 of a mile. At what unit rate is the turtle crawling?

Answer 1

To find the unit rate at which the turtle is crawling, we need to determine how far the turtle travels per hour.

The turtle travels \( \frac{3}{20} \) of a mile in \( \frac{5}{6} \) of an hour.

To find the rate in miles per hour, we can set up the following proportion to calculate how far the turtle would go in one hour:

\[
\text{Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{3/20 \text{ miles}}{5/6 \text{ hours}}
\]

To divide by a fraction, we multiply by its reciprocal:

\[
\text{Rate} = \frac{3/20}{5/6} = \frac{3}{20} \times \frac{6}{5}
\]

Now we can multiply the fractions:

\[
\text{Rate} = \frac{3 \times 6}{20 \times 5} = \frac{18}{100}
\]

To simplify \( \frac{18}{100} \):

We can divide the numerator and the denominator by their greatest common divisor, which is 2:

\[
\frac{18 \div 2}{100 \div 2} = \frac{9}{50}
\]

Thus, the unit rate at which the turtle is crawling is

\[
\frac{9}{50} \text{ miles per hour}.
\]