Question

Solve this multi-step problem. A runner completes 1/4 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?

Answer 1

To solve the problem, we first need to determine the runner's pace and then calculate how far the runner can go in 16 minutes.

1. **Find the distance covered in 8 minutes:**
The runner completes \( \frac{1}{4} \) of a 5-mile race in 8 minutes. We can calculate the distance covered in that time:

\[
\text{Distance in 8 minutes} = \frac{1}{4} \times 5 \text{ miles} = \frac{5}{4} \text{ miles} = 1.25 \text{ miles}
\]

2. **Calculate the pace:**
The pace can be calculated as the distance per minute:

\[
\text{Pace} = \frac{1.25 \text{ miles}}{8 \text{ minutes}} = 0.15625 \text{ miles/minute}
\]

3. **Calculate the distance for 16 minutes:**
Now, we can use the pace to find out how far the runner can go in 16 minutes:

\[
\text{Distance in 16 minutes} = \text{Pace} \times \text{Time}
\]
\[
\text{Distance in 16 minutes} = 0.15625 \text{ miles/minute} \times 16 \text{ minutes}
\]
\[
\text{Distance in 16 minutes} = 2.5 \text{ miles}
\]

Therefore, at the same pace, the runner can go **2.5 miles** in 16 minutes.