7. The tables below show the number of jumping jacks completed after a given period of time in minutes. Kimberly Time (min) # Jumping Jacks 3 28 8 58 12 82 16 106 Katrina Time (min) # Jumping Jacks 2 16 5 40 12 96 20 160
The rate at which Kimberly completes jumping jacks can be calculated by dividing the change in the number of jumping jacks by the change in time.
For the time period from 3 minutes to 8 minutes:
Rate = (58 - 28) / (8 - 3) = 30 / 5 = 6 jumping jacks per minute
For the time period from 8 minutes to 12 minutes:
Rate = (82 - 58) / (12 - 8) = 24 / 4 = 6 jumping jacks per minute
For the time period from 12 minutes to 16 minutes:
Rate = (106 - 82) / (16 - 12) = 24 / 4 = 6 jumping jacks per minute
Therefore, Kimberly completes jumping jacks at a constant rate of 6 jumping jacks per minute.
Similarly, we can calculate the rate at which Katrina completes jumping jacks for each time period.
For the time period from 2 minutes to 5 minutes:
Rate = (40 - 16) / (5 - 2) = 24 / 3 = 8 jumping jacks per minute
For the time period from 5 minutes to 12 minutes:
Rate = (96 - 40) / (12 - 5) = 56 / 7 = 8 jumping jacks per minute
For the time period from 12 minutes to 20 minutes:
Rate = (160 - 96) / (20 - 12) = 64 / 8 = 8 jumping jacks per minute
Therefore, Katrina completes jumping jacks at a constant rate of 8 jumping jacks per minute.
What would you like to know or do with this information?
To find the rate at which jumping jacks are completed per minute, you need to calculate the rate of change. The rate of change is determined by dividing the change in the number of jumping jacks by the change in time.
For Kimberly:
- The change in time is 16 minutes - 3 minutes = 13 minutes.
- The change in the number of jumping jacks is 106 - 28 = 78 jumping jacks.
Rate of change for Kimberly = Change in the number of jumping jacks / Change in time
Rate of change for Kimberly = 78 / 13 = 6 jumping jacks per minute.
For Katrina:
- The change in time is 20 minutes - 2 minutes = 18 minutes.
- The change in the number of jumping jacks is 160 - 16 = 144 jumping jacks.
Rate of change for Katrina = Change in the number of jumping jacks / Change in time
Rate of change for Katrina = 144 / 18 = 8 jumping jacks per minute.
Therefore, Kimberly completes 6 jumping jacks per minute, and Katrina completes 8 jumping jacks per minute.