Sure, let's start with the given information and work through it step-by-step.
### Problem
Sophie jogs [tex]\(4 \frac{1}{4}\)[/tex] miles in [tex]\(\frac{7}{8}\)[/tex] hour. How far would she run in [tex]\(4 \frac{1}{2}\)[/tex] hours if she kept the same pace?
### Step-by-Step Solution
1. Convert Mixed Numbers to Improper Fractions
- Sophie jogs [tex]\(4 \frac{1}{4}\)[/tex] miles.
[tex]\[
4 \frac{1}{4} = 4 + \frac{1}{4} = \frac{16}{4} + \frac{1}{4} = \frac{17}{4}
\][/tex]
- The time is [tex]\(\frac{7}{8}\)[/tex] hour.
2. Calculate Sophie's Pace (miles per hour)
- To find the pace (miles per hour), we divide the distance by the time.
[tex]\[
\text{Pace} = \frac{\frac{17}{4}}{\frac{7}{8}}
\][/tex]
- Division by a fraction is the same as multiplying by its reciprocal.
[tex]\[
\text{Pace} = \frac{17}{4} \times \frac{8}{7} = \frac{17 \times 8}{4 \times 7} = \frac{136}{28} = 4.857142857142857 \, \text{miles per hour}
\][/tex]
3. Convert the Desired Time to an Improper Fraction
- The desired time is [tex]\(4 \frac{1}{2}\)[/tex] hours.
[tex]\[
4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2}
\][/tex]
4. Calculate the Distance for [tex]\(4 \frac{1}{2}\)[/tex] Hours
- Use the pace to find the distance she would run in [tex]\(4 \frac{1}{2}\)[/tex] hours.
[tex]\[
\text{Distance} = \text{Pace} \times \text{Time} = 4.857142857142857 \times 4.5
\][/tex]
- Multiplying these values, we get:
[tex]\[
\text{Distance} = 21.857142857142854 \, \text{miles}
\][/tex]
### Conclusion
If Sophie keeps the same pace, she would run approximately [tex]\(21.857142857142854\)[/tex] miles in [tex]\(4 \frac{1}{2}\)[/tex] hours.
