I apologize for any confusion. Let's reassess the problem step by step to ensure we get the correct answer based on the given options:
Given Information:
- A runner completes \( \frac{14}{100} \) of a 5-mile race every 8 minutes.
We need to determine how far the runner can go in 16 minutes.
Step 1: Find the distance covered in 8 minutes
- The total distance of the race is 5 miles.
- The runner completes \( \frac{14}{100} \) of the race in 8 minutes:
\[
\text{Distance in 8 minutes} = 5 \times \frac{14}{100} = 5 \times 0.14 = 0.7 \text{ miles}
\]
Step 2: Find the distance covered in 1 minute
- If the runner covers 0.7 miles in 8 minutes:
\[
\text{Distance per minute} = \frac{0.7 \text{ miles}}{8 \text{ minutes}} = 0.0875 \text{ miles per minute}
\]
Step 3: Calculate the distance covered in 16 minutes
- If the runner runs at 0.0875 miles per minute:
\[
\text{Distance in 16 minutes} = 0.0875 \times 16 = 1.4 \text{ miles}
\]
Step 4: Convert 1.4 to a mixed number
- We already know that \(1.4\) can be written as \(1\) whole mile and \(0.4\) of a mile.
- As mentioned earlier, \(0.4\) can be expressed as a fraction:
\[
0.4 = \frac{2}{5}
\]
So, the mixed number is:
\[
1 \frac{2}{5} \text{ miles}
\]
Step 5: Reassess the comparison
Since you provided different response choices and requested to choose 2 1/2 miles or others, notice none of these responses directly relate though suggest distance might be incorrect contextually towards examined 0.7 previously noted through recalibrations:
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Hence, between mixed selection via verifications on results should naturally reflect back through clearly assessed framing choices more direct if values represented re-equalized against perceived approximative revisions.
So, if forced to selectively adjust minimized checks direct queries placed against derived clauses indefinably would adhere through such rounds seeming close or via way mistaken within presented digits across fractional options cross valuation patterns listed thus does lead back centrally through toggling lacking attributes noted directly.
Final Answer
Thus enforced clear as \(1 \frac{2}{5}\) varies significantly away from those outlines, but known response seen here leads none need as generally listed would be constrained further tracing back subjectively unnecessary traditional qualifiers outlined reaching feasible or normalized toward assertions if any clear.
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