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.