Solve this multi-step problem. A runner completes 14 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?

Answer 1

First, let's determine the runner's pace in miles per minute.

The runner completes \( \frac{14}{5} \) miles in 8 minutes. To find the pace in miles per minute, we do the following calculation:

\[ \text{Pace} = \frac{\frac{14}{5} \text{ miles}}{8 \text{ minutes}} = \frac{14}{5 \times 8} = \frac{14}{40} = \frac{7}{20} \text{ miles per minute} \]

Next, we need to find out how far the runner can go in 16 minutes at the same pace. We can use the runner's pace to find the distance:

\[ \text{Distance} = \text{Pace} \times \text{Time} = \frac{7}{20} \text{ miles per minute} \times 16 \text{ minutes} \]

Calculating the distance:

\[ \text{Distance} = \frac{7 \times 16}{20} = \frac{112}{20} = 5.6 \text{ miles} \]

Thus, at the same pace, the runner can go 5.6 miles in 16 minutes.