To analyze the performance of Kimberly and Katrina in terms of the number of jumping jacks completed over time, we can take a closer look at the data provided in the tables.
Kimberly's Performance:
- At 3 seconds: 17 jumping jacks
- At 8 seconds: 37 jumping jacks
- At 12 seconds: 53 jumping jacks
- At 16 seconds: 69 jumping jacks
Katrina's Performance:
- At 2 seconds: 10 jumping jacks
- At 5 seconds: 25 jumping jacks
- At 12 seconds: 60 jumping jacks
- At 20 seconds: 100 jumping jacks
Analysis
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Calculating the Rate of Jumping Jacks: To understand how quickly each person is completing jumping jacks, we can calculate the rate (jumping jacks per second) over the relevant time intervals.
Kimberly:
- From 3 to 8 seconds: \[ \text{Rate} = \frac{37 - 17}{8 - 3} = \frac{20}{5} = 4 \text{ jacks/second} \]
- From 8 to 12 seconds: \[ \text{Rate} = \frac{53 - 37}{12 - 8} = \frac{16}{4} = 4 \text{ jacks/second} \]
- From 12 to 16 seconds: \[ \text{Rate} = \frac{69 - 53}{16 - 12} = \frac{16}{4} = 4 \text{ jacks/second} \]
Kimberly maintains a consistent rate of 4 jumping jacks per second.
Katrina:
- From 2 to 5 seconds: \[ \text{Rate} = \frac{25 - 10}{5 - 2} = \frac{15}{3} = 5 \text{ jacks/second} \]
- From 5 to 12 seconds: \[ \text{Rate} = \frac{60 - 25}{12 - 5} = \frac{35}{7} = 5 \text{ jacks/second} \]
- From 12 to 20 seconds: \[ \text{Rate} = \frac{100 - 60}{20 - 12} = \frac{40}{8} = 5 \text{ jacks/second} \]
Katrina maintains a consistent rate of 5 jumping jacks per second.
Conclusion:
- Kimberly completes jumping jacks at a rate of 4 jacks/second.
- Katrina completes jumping jacks at a rate of 5 jacks/second.
Thus, over the time periods measured, Katrina completes jumping jacks faster than Kimberly.
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