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)

Responses

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

160 miles
2/12 miles
2 Start Fraction 1 over 2 End Fraction miles
1/8
18 mile

1 answer

To find out how far the runner can go in 16 minutes at the same pace, 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. \[ \text{Distance covered in 8 minutes} = \frac{1}{4} \times 5 = \frac{5}{4} \text{ miles} \]

  2. Next, we find the runner's speed: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{5}{4} \text{ miles}}{8 \text{ minutes}} = \frac{5}{32} \text{ miles per minute} \]

  3. Now we can determine how far the runner can go in 16 minutes: \[ \text{Distance in 16 minutes} = \text{Speed} \times \text{Time} = \frac{5}{32} \text{ miles per minute} \times 16 \text{ minutes} \] \[ = \frac{5 \times 16}{32} = \frac{80}{32} = \frac{5}{2} \text{ miles} = 2 \frac{1}{2} \text{ miles} \]

Thus, the runner can go \( 2 \frac{1}{2} \) miles in 16 minutes.

The correct response is: 2 Start Fraction 1 over 2 End Fraction miles.