To solve the problem, we first need to determine the runner's pace.
The runner completes 14 of a 5-mile race every 8 minutes. This means the runner runs:
\[ 5 \text{ miles} \div 14 = \frac{5}{14} \text{ miles per unit} \]
Next, we can calculate the runner's speed in miles per minute:
- The total time taken for the race is 8 minutes.
- The distance covered in that time is 5 miles.
To find the speed in miles per minute, we divide the distance by the total time spent:
\[ \text{Speed} = \frac{5 \text{ miles}}{8 \text{ minutes}} = \frac{5}{8} \text{ miles per minute} \]
Now, we need to determine how far the runner can go in 16 minutes. We can use the runner's speed to calculate the distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \] \[ \text{Distance} = \frac{5}{8} \text{ miles per minute} \times 16 \text{ minutes} \]
Calculating this gives:
\[ \text{Distance} = \frac{5 \times 16}{8} = \frac{80}{8} = 10 \text{ miles} \]
From the options provided:
- 110 mile
- Start Fraction 1 over 10 End Fraction mile
- 18 mile
- Start Fraction 1 over 8 End Fraction mile
- 212 miles
- 2 Start Fraction 1 over 2 End Fraction miles
- 160 miles
There isn't a direct match for 10 miles, which indicates that there might be a typo in the options. However, 10 miles is the correct answer based on the calculations.
Thus, in 16 minutes, the runner can travel 10 miles.