The problem asks how many hours it will take Clay to run 5$\frac{1}{3}$ laps around the track, given that one lap takes $\frac{1}{4}$ of an hour.

Solution:

1. Clay's time per lap: We know that one lap takes $\frac{1}{4}$ hours.

2. Total laps: Clay needs to run 5$\frac{1}{3}$ laps, which we convert into an improper fraction: $5\frac{1}{3} = \frac{16}{3}$

3. Time for 5$\frac{1}{3}$ laps: To find the total time, multiply the time per lap ($\frac{1}{4}$) by the total number of laps ($\frac{16}{3}$): $\text{Total time} = \frac{1}{4} \times \frac{16}{3} = \frac{16}{12} = \frac{4}{3} \text{ hours}$

   Therefore, it will take Clay $\frac{4}{3}$ hours or 1$\frac{1}{3}$ hours to run 5$\frac{1}{3}$ laps around the track.

Would you like further explanation or details on this? Here are some related questions:

1. How can you convert mixed numbers to improper fractions?
2. What is the process of multiplying fractions?
3. How can you simplify complex fractions?
4. Why is it important to convert mixed numbers in problems like these?
5. What is the difference between a mixed number and an improper fraction?

Tip: When multiplying fractions, always simplify the result at the end by dividing both the numerator and denominator by their greatest common factor (GCF).