Question
A runner calculated her average speed during a half-marathon.
The average speed of the runner was 1.9 × 10-3
per
.
The average speed of the runner was 1.9 × 10-3
per
.
Answers
GPT-4o mini
It looks like your message got cut off. However, I can help you clarify the concept of average speed in the context of a half-marathon.
To compute the average speed:
1. **Half-Marathon Distance**: A half-marathon is 13.1 miles or approximately 21.1 kilometers.
2. **Average Speed Formula**: Average speed is calculated using the formula:
\[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
\]
If the average speed of the runner is given as \( 1.9 \times 10^{-3} \) (units are not specified, but let’s assume it's in miles per second), we can convert that speed to more practical units, like miles per hour (mph) or kilometers per hour (km/h), and analyze how long it would take to complete the half-marathon.
### Conversion Example
1. **Convert from miles per second to miles per hour**:
\[
1.9 \times 10^{-3} \text{ miles/second} \times 3600 \text{ seconds/hour} = 6.84 \text{ miles/hour}
\]
2. **Time taken to complete the half-marathon**:
Using the average speed:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{13.1 \text{ miles}}{6.84 \text{ miles/hour}} \approx 1.92 \text{ hours} \approx 115.2 \text{ minutes}
\]
### Conclusion
Thus, with an average speed of \( 1.9 \times 10^{-3} \) miles per second, it would take approximately 1.92 hours or about 115.2 minutes to complete a half-marathon.
If you meant something else or need further calculations with different units, please let me know!
To compute the average speed:
1. **Half-Marathon Distance**: A half-marathon is 13.1 miles or approximately 21.1 kilometers.
2. **Average Speed Formula**: Average speed is calculated using the formula:
\[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
\]
If the average speed of the runner is given as \( 1.9 \times 10^{-3} \) (units are not specified, but let’s assume it's in miles per second), we can convert that speed to more practical units, like miles per hour (mph) or kilometers per hour (km/h), and analyze how long it would take to complete the half-marathon.
### Conversion Example
1. **Convert from miles per second to miles per hour**:
\[
1.9 \times 10^{-3} \text{ miles/second} \times 3600 \text{ seconds/hour} = 6.84 \text{ miles/hour}
\]
2. **Time taken to complete the half-marathon**:
Using the average speed:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{13.1 \text{ miles}}{6.84 \text{ miles/hour}} \approx 1.92 \text{ hours} \approx 115.2 \text{ minutes}
\]
### Conclusion
Thus, with an average speed of \( 1.9 \times 10^{-3} \) miles per second, it would take approximately 1.92 hours or about 115.2 minutes to complete a half-marathon.
If you meant something else or need further calculations with different units, please let me know!