To solve the problem, we'll follow these steps:
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First, determine how far the runner completes in 8 minutes.
- The race is 5 miles long, and the runner completes \( \frac{1}{4} \) of the race every 8 minutes.
- So, the distance completed in 8 minutes is \( \frac{1}{4} \times 5 \) miles, which is \( 1.25 \) miles.
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Next, determine how far the runner goes in 16 minutes.
- Since the runner completes \( 1.25 \) miles in 8 minutes, in 16 minutes (which is double the time), the runner will complete double the distance.
- Therefore, the distance covered in 16 minutes would be \( 2 \times 1.25 \) miles, which is \( 2.5 \) miles.
Thus, the runner can go 2.5 miles in 16 minutes.
Given the options:
- 2 1/2 (which is the same as 2.5 miles)
- 160 miles
- 1/10 miles
- 1/8 miles
The correct answer is 2 1/2.