The tables below show the number of jumping jacks completed after a given period of time in seconds.

Question

Kimberly:
Time (seconds) | Jumping Jacks
3 | 17
8 | 37
12 | 53
16 | 69
Katrina:
Time (seconds) | Jumping Jacks
2 | 10
5 | 25
12 | 60
20 | 100
a. Which person is doing more jumping jacks per second? _______
b. Which person had done more jumping jacks initially before the timer started? ________
c. Which person shows a proportional relationship? _________
Part 1
A. Kimberly
B. Katrina
C. Neither
D. Both
Part 2
A. Kimberly
B. Katrina
C. Neither
D. Both
Part 3
A. Kimberly
B. Katrina
C. Neither
D. Both

Answer 1

To answer your questions, let's analyze the data for both Kimberly and Katrina.

Part 1: Jumping Jacks per Second

To find out who is doing more jumping jacks per second, we can calculate the rate of jumping jacks per second for both individuals at various time points.

Kimberly's Rates of Jumping Jacks per Second:

1. From 0 to 3 seconds: \( \frac{17 - 0}{3 - 0} = \frac{17}{3} \approx 5.67 \)
2. From 0 to 8 seconds: \( \frac{37 - 0}{8 - 0} = \frac{37}{8} = 4.625 \)
3. From 0 to 12 seconds: \( \frac{53 - 0}{12 - 0} = \frac{53}{12} \approx 4.42 \)
4. From 0 to 16 seconds: \( \frac{69 - 0}{16 - 0} = \frac{69}{16} = 4.3125 \)

Katrina's Rates of Jumping Jacks per Second:

1. From 0 to 2 seconds: \( \frac{10 - 0}{2 - 0} = \frac{10}{2} = 5 \)
2. From 0 to 5 seconds: \( \frac{25 - 0}{5 - 0} = \frac{25}{5} = 5 \)
3. From 0 to 12 seconds: \( \frac{60 - 0}{12 - 0} = \frac{60}{12} = 5 \)
4. From 0 to 20 seconds: \( \frac{100 - 0}{20 - 0} = \frac{100}{20} = 5 \)

Comparison:

• Kimberly's average rates fluctuated, but were mostly declining: 5.67, 4.625, 4.42, and 4.3125.
• Katrina consistently maintained a rate of 5 jumping jacks per second.

Answer for Part 1: Katrina is doing more jumping jacks per second.

Part 2: Initial Jumping Jacks

To determine who had completed more jumping jacks initially (before the timer started), we look at the data provided. Both tables show jumping jacks starting from 0.

Answer for Part 2: Neither person had done any jumping jacks before the timer started.

Part 3: Proportional Relationship

A proportional relationship exists when the ratio between two quantities remains constant. In this case, we have to look for these characteristics in the data:

• Kimberly's Data:

  • The relationship varies (as calculated above), so Kimberly's performance is not proportional.

• Katrina's Data:

  • The rates of jumping jacks per second are consistent and constant at 5 throughout the measured times, indicating proportionality.

Answer for Part 3: Katrina shows a proportional relationship.

Summary of Answers:

a. B (Katrina) b. C (Neither) c. B (Katrina)