a. To determine which person is doing more jumping jacks per second, we can calculate the rate of jumping jacks per second for both Kimberly and Katrina.
Kimberly:
- For 3 seconds: 17 jumping jacks → \( \frac{17}{3} \approx 5.67 \) jacks/second
- For 8 seconds: 37 jumping jacks → \( \frac{37}{8} = 4.625 \) jacks/second
- For 12 seconds: 53 jumping jacks → \( \frac{53}{12} \approx 4.42 \) jacks/second
- For 16 seconds: 69 jumping jacks → \( \frac{69}{16} \approx 4.31 \) jacks/second
Katrina:
- For 2 seconds: 10 jumping jacks → \( \frac{10}{2} = 5 \) jacks/second
- For 5 seconds: 25 jumping jacks → \( \frac{25}{5} = 5 \) jacks/second
- For 12 seconds: 60 jumping jacks → \( \frac{60}{12} = 5 \) jacks/second
- For 20 seconds: 100 jumping jacks → \( \frac{100}{20} = 5 \) jacks/second
The average jumping jacks per second for Kimberly is decreasing, while Katrina maintains an average of 5 jumping jacks per second.
Answer: Katrina
b. To determine who had done more jumping jacks initially before the timer started, we look at the data provided. However, the data does not specify any jumping jacks done before the timer started for either person. Based on the given data, we cannot conclude anything.
Answer: Neither
c. To determine who shows a proportional relationship, we consider whether the jumping jacks are increasing consistently over time.
Katrina's jumping jacks numbers are consistent and show a linear progression:
- At 2 seconds: 10 jumping jacks
- At 5 seconds: 25 jumping jacks (increased by 15)
- At 12 seconds: 60 jumping jacks (increased by 35)
- At 20 seconds: 100 jumping jacks (increased by 40)
The increases in each interval are consistent in ratio to their time intervals.
In contrast, Kimberly's jumping jacks numbers do not show the same linear pattern, as the increases are varied.
Answer: Katrina
Final Responses:
a. Katrina
b. Neither
c. Katrina
1 answer