Question

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

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(3 points)

Answer 1

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

1. **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.