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 calculate the speeds of Perry and Powell in miles per second, we first need to convert their times into seconds.

### Perry's Time
Perry's time is 7 minutes and 30 seconds:

\[
7 \text{ minutes} = 7 \times 60 = 420 \text{ seconds}
\]
Adding the additional 30 seconds gives:

\[
420 + 30 = 450 \text{ seconds}
\]

### Powell's Time
Powell's time is 8 minutes:

\[
8 \text{ minutes} = 8 \times 60 = 480 \text{ seconds}
\]

### Speed Calculation
Speed in miles per second (mps) can be calculated using the formula:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

#### Perry's Speed
- Distance: \( \frac{3}{4} \) mile
- Time: 450 seconds

\[
\text{Speed}_{\text{Perry}} = \frac{\frac{3}{4}}{450}
\]
\[
= \frac{3}{4 \times 450}
= \frac{3}{1800}
= 0.00166667 \text{ miles per second}
\]
Approximately, Perry's speed is **0.00167 mps**.

#### Powell's Speed
- Distance: \( \frac{3}{4} \) mile
- Time: 480 seconds

\[
\text{Speed}_{\text{Powell}} = \frac{\frac{3}{4}}{480}
\]
\[
= \frac{3}{4 \times 480}
= \frac{3}{1920}
= 0.0015625 \text{ miles per second}
\]
Approximately, Powell's speed is **0.00156 mps**.

### Final Speeds
- Perry: **0.00167 mps**
- Powell: **0.00156 mps**

When looking at the options provided, it is clear that the closest match is:

**0.0017 mps, 0.0015 mps**