To find out how far the runner can go in 16 minutes, we first need to determine the pace of the runner based on the information given.
The runner completes \( \frac{1}{4} \) of a 5-mile race in 8 minutes. First, we calculate how far that is:
\[ \frac{1}{4} \times 5 \text{ miles} = \frac{5}{4} \text{ miles} = 1.25 \text{ miles} \]
So, the runner covers 1.25 miles in 8 minutes.
To find the pace in miles per minute, we divide the distance by the time:
\[ \text{Pace} = \frac{1.25 \text{ miles}}{8 \text{ minutes}} = 0.15625 \text{ miles per minute} \]
Now, we want to find out how far the runner can go in 16 minutes. We can use the pace calculated above:
\[ \text{Distance in 16 minutes} = \text{Pace} \times \text{Time} \] \[ \text{Distance} = 0.15625 \text{ miles per minute} \times 16 \text{ minutes} = 2.5 \text{ miles} \]
Therefore, in 16 minutes, the runner can go \( 2.5 \) miles.
The answer to the problem is:
2 1/2 miles (option: 2 Start Fraction 1 over 2 End Fraction miles).