Question

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?(1 point)
Responses

110 mile
Start Fraction 1 over 10 End Fraction mile

18 mile
Start Fraction 1 over 8 End Fraction mile

212 miles
2 Start Fraction 1 over 2 End Fraction miles

160 miles
160 miles

Answer 1

To solve the problem, we first need to determine the runner's pace.

The runner completes 14 of a 5-mile race every 8 minutes. This means the runner runs:

\[
5 \text{ miles} \div 14 = \frac{5}{14} \text{ miles per unit}
\]

Next, we can calculate the runner's speed in miles per minute:

1. The total time taken for the race is 8 minutes.
2. The distance covered in that time is 5 miles.

To find the speed in miles per minute, we divide the distance by the total time spent:

\[
\text{Speed} = \frac{5 \text{ miles}}{8 \text{ minutes}} = \frac{5}{8} \text{ miles per minute}
\]

Now, we need to determine how far the runner can go in 16 minutes. We can use the runner's speed to calculate the distance:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
\[
\text{Distance} = \frac{5}{8} \text{ miles per minute} \times 16 \text{ minutes}
\]

Calculating this gives:

\[
\text{Distance} = \frac{5 \times 16}{8} = \frac{80}{8} = 10 \text{ miles}
\]

From the options provided:

- 110 mile
- Start Fraction 1 over 10 End Fraction mile
- 18 mile
- Start Fraction 1 over 8 End Fraction mile
- 212 miles
- 2 Start Fraction 1 over 2 End Fraction miles
- 160 miles

There isn't a direct match for 10 miles, which indicates that there might be a typo in the options. However, 10 miles is the correct answer based on the calculations.

Thus, in 16 minutes, the runner can travel **10 miles**.