Final answer:
To find the average hourly change in tub fullness, subtract the amount left at the end from the amount at the start and divide by the number of hours.
Step-by-step explanation:
To find the average hourly change in tub fullness, we need to determine how much the tub is decreasing in fullness over the 6 1/2 hour shift.
First, let's find the difference in fullness between the start and end of the shift. We subtract 1/6 (the amount left at the end) from 2/3 (the amount at the start) to get 2/3 - 1/6 = 4/6 - 1/6 = 3/6 = 1/2.
Next, we need to find the change in fullness per hour. We divide the difference in fullness (1/2) by the number of hours (6 1/2) to get 1/2 ÷ 6 1/2 = 1/2 ÷ 13/2 = 1/2 × 2/13 = 1/13.
So, the average hourly change in tub fullness is 1/13.