Question

Clarissa cycled 12 1/2 miles per hour for 2 1/2 hours. How far did she travel, write the answer as an improper fraction in simplest form

Answer 1

To determine how far Clarissa traveled, we can multiply her speed by the time she cycled.

1. **Convert the mixed numbers to improper fractions.**
- Clarissa's speed:
\[
12 \frac{1}{2} = 12 + \frac{1}{2} = \frac{24}{2} + \frac{1}{2} = \frac{25}{2} \text{ miles per hour}
\]

- The time:
\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \text{ hours}
\]

2. **Multiply the speed by the time to find the distance.**
\[
\text{Distance} = \text{Speed} \times \text{Time} = \left(\frac{25}{2}\right) \times \left(\frac{5}{2}\right)
\]

Multiplying these fractions:
\[
\text{Distance} = \frac{25 \times 5}{2 \times 2} = \frac{125}{4}
\]

3. **Convert the improper fraction to simplest form.**
The fraction \(\frac{125}{4}\) is already in simplest form as 125 and 4 have no common factors (aside from 1).

Thus, the total distance Clarissa traveled is:
\[
\boxed{\frac{125}{4}} \text{ miles}
\]