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?(1 point)

Question

Responses

1/8 mile
Start Fraction 1 over 8 End Fraction mile

2 1/2 miles
2 Start Fraction 1 over 2 End Fraction miles

1/10 mile
Start Fraction 1 over 10 End Fraction mile

160 miles

Answer 1

To solve this problem, we first need to determine the runner's pace based on the information given.

1. The runner completes \( \frac{1}{4} \) of a 5-mile race in 8 minutes.

First, we calculate how far the runner has gone in miles:

\[ \frac{1}{4} \text{ of } 5 = \frac{5}{4} \text{ miles} \]

Now, we can find the runner's speed in miles per minute:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{5}{4} \text{ miles}}{8 \text{ minutes}} = \frac{5}{32} \text{ miles per minute} \]

2. Next, we want to determine how far the runner can go in 16 minutes. We can use the speed we just calculated.

The distance for 16 minutes at the pace of \( \frac{5}{32} \) miles per minute is:

\[ \text{Distance} = \text{Speed} \times \text{Time} = \frac{5}{32} \text{ miles per minute} \times 16 \text{ minutes} \]

Calculating this gives:

\[ \text{Distance} = \frac{5 \times 16}{32} = \frac{80}{32} = 2.5 \text{ miles} \]

Thus, the runner can go \( 2.5 \) miles in 16 minutes.

The correct answer is:

2 1/2 miles (or \( 2.5 \) miles).