Question

Perry and Powell each did a solo run of 3/4 mile. Perry was timed at 7 minutes and 30 seconds while Powell was timed at 8 minutes. What is the unit rate (speed) for each runner in miles per second (mps)?
0.0017 mps, 0.0015 mps
0.0017 mps, 0.0016 mps
0.0018 mps, 0.0017 mps
800 mps, 853 mps

Answer 1

To find the speed of each runner in miles per second (mps), we first need to convert their times from minutes and seconds to seconds.

1. **Perry's Time:**
- Perry's time is 7 minutes and 30 seconds.
- Convert this to seconds:
\[
7 \text{ minutes} = 7 \times 60 = 420 \text{ seconds}
\]
\[
\text{Total time for Perry} = 420 + 30 = 450 \text{ seconds}
\]

- Speed in miles per second (mps):
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{3/4 \text{ mile}}{450 \text{ seconds}} = \frac{0.75}{450}
\]
\[
\text{Speed} = 0.0016667 \text{ miles per second}
\]
\[
\text{Speed} \approx 0.0017 \text{ mps}
\]

2. **Powell's Time:**
- Powell's time is 8 minutes.
- Convert this to seconds:
\[
8 \text{ minutes} = 8 \times 60 = 480 \text{ seconds}
\]

- Speed in miles per second (mps):
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{3/4 \text{ mile}}{480 \text{ seconds}} = \frac{0.75}{480}
\]
\[
\text{Speed} = 0.0015625 \text{ miles per second}
\]
\[
\text{Speed} \approx 0.0016 \text{ mps}
\]

Thus, the speeds of Perry and Powell in miles per second are approximately:
- Perry: 0.0017 mps
- Powell: 0.0016 mps

The answer is:
**0.0017 mps, 0.0016 mps**.