To find out how far the runner can go in 16 minutes at the same pace, we first need to determine the runner's pace based on the information provided.
The runner completes \( \frac{1}{4} \) of a 5-mile race in 8 minutes. We calculate how far the runner runs in that time:
\[ \frac{1}{4} \times 5 \text{ miles} = \frac{5}{4} \text{ miles} = 1.25 \text{ miles} \]
Now, we need to find the runner's pace in miles per minute:
\[ \text{Pace} = \frac{1.25 \text{ miles}}{8 \text{ minutes}} = 0.15625 \text{ miles per minute} \]
Next, we calculate how far the runner would go in 16 minutes:
\[ \text{Distance in 16 minutes} = \text{Pace} \times 16 = 0.15625 \text{ miles per minute} \times 16 \text{ minutes} = 2.5 \text{ miles} \]
Thus, the runner can go 2.5 miles in 16 minutes.
The correct answer is:
2 1/2 miles.