Which situation has a unit rate of 15 laps per hour?
Luigi runs 44 laps in 4 hour
B. Luigi runs 2 laps in 30 hours
C. Luigi runs 150 laps in 10 hours
D. Luigi runs 60 laps in 5 hours
The Correct Answer and Explanation is:
To determine which situation has a unit rate of 15 laps per hour, we need to calculate the rate for each option given. A unit rate is found by dividing the total quantity (in this case, laps) by the total time (in hours). Let’s analyze each option:
A. Luigi runs 44 laps in 4 hours
To find the unit rate:
[
\text{Unit rate} = \frac{44 \text{ laps}}{4 \text{ hours}} = 11 \text{ laps per hour}
]
B. Luigi runs 2 laps in 30 hours
Calculating the unit rate:
[
\text{Unit rate} = \frac{2 \text{ laps}}{30 \text{ hours}} = \frac{1}{15} \text{ laps per hour} \approx 0.067 \text{ laps per hour}
]
C. Luigi runs 150 laps in 10 hours
Finding the unit rate:
[
\text{Unit rate} = \frac{150 \text{ laps}}{10 \text{ hours}} = 15 \text{ laps per hour}
]
D. Luigi runs 60 laps in 5 hours
Calculating the unit rate:
[
\text{Unit rate} = \frac{60 \text{ laps}}{5 \text{ hours}} = 12 \text{ laps per hour}
]
Summary of Unit Rates
- Option A: 11 laps/hour
- Option B: Approximately 0.067 laps/hour
- Option C: 15 laps/hour
- Option D: 12 laps/hour
Conclusion
The correct answer is C. Luigi runs 150 laps in 10 hours, which gives him a unit rate of 15 laps per hour. This unit rate is calculated by dividing the total number of laps run (150) by the total time taken (10 hours), confirming that option C meets the criteria specified in the question.
Understanding unit rates is crucial in various applications, including comparing speeds and efficiency in running, as it provides a standardized measure that allows for easier comparisons between different quantities or rates. In this example, by breaking down each situation mathematically, we find that option C is the only scenario that meets the required rate of 15 laps per hour, illustrating the importance of careful calculations in problem-solving.