To find the distance that Clarissa traveled, we can use the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
First, we need to convert the speed and time from mixed numbers to improper fractions.
Speed:
- \( 12 \frac{1}{2} \) can be converted to an improper fraction as follows: \[ 12 \frac{1}{2} = \frac{2 \times 12 + 1}{2} = \frac{24 + 1}{2} = \frac{25}{2} \text{ miles per hour} \]
Time:
- \( 2 \frac{1}{2} \) can be converted to an improper fraction as follows: \[ 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \text{ hours} \]
Now, we can substitute these values into the distance formula:
\[ \text{Distance} = \left(\frac{25}{2}\right) \times \left(\frac{5}{2}\right) \]
Now, multiply the two fractions:
\[ \text{Distance} = \frac{25 \times 5}{2 \times 2} = \frac{125}{4} \text{ miles} \]
Now, the distance traveled by Clarissa is:
\[ \frac{125}{4} \text{ miles} \]
The improper fraction \(\frac{125}{4}\) is already in simplest form.
Thus, the answer is:
\[ \frac{125}{4} \]