Question

Clarissa cycled at 12 1/2 miles per hour for 2 1/2 hours. How far did she travel? Your answer should be written as an improper fraction in simplest form.

Answer 1

To find the distance traveled by Clarissa, we can use the formula for distance:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

First, we convert the speed and time into improper fractions.

1. **Convert speed (12 1/2 miles per hour) to an improper fraction**:
- \( 12 \frac{1}{2} = 12 + \frac{1}{2} = \frac{24}{2} + \frac{1}{2} = \frac{25}{2} \) miles per hour.

2. **Convert time (2 1/2 hours) to an improper fraction**:
- \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \) hours.

Now we can substitute these values into the distance formula:

\[
\text{Distance} = \left(\frac{25}{2}\right) \times \left(\frac{5}{2}\right)
\]

To multiply the fractions:

\[
\text{Distance} = \frac{25 \times 5}{2 \times 2} = \frac{125}{4}
\]

The distance Clarissa traveled is:

\[
\frac{125}{4} \text{ miles}
\]

Finally, we check if the fraction \(\frac{125}{4}\) is in simplest form. The numerator 125 and the denominator 4 have no common factors other than 1, so it is already in simplest form.

Thus, the final answer is:

\[
\frac{125}{4} \text{ miles}
\]