Answer:
![-1/13\text{ tub per hour}](https://tex.z-dn.net/?f=-1%2F13%5Ctext%7B%20tub%20per%20hour%7D)
Step-by-step explanation:
First, let's find how much of the tub was used within the time.
We know that the tub was 2/3 full was Jenna started.
And it was only 1/6 full when Jenna ended.
Therefore, to find the amount used, we can subtract 1/6 from 2/3. So:
![u=\frac{2}{3}-\frac{1}{6}](https://tex.z-dn.net/?f=u%3D%5Cfrac%7B2%7D%7B3%7D-%5Cfrac%7B1%7D%7B6%7D)
Make a common denominator. Change 2/3 to 4/6 by multiplying both layers by 2. So:
![u=\frac{4}{6}-\frac{1}{6}](https://tex.z-dn.net/?f=u%3D%5Cfrac%7B4%7D%7B6%7D-%5Cfrac%7B1%7D%7B6%7D)
Subtract and reduce:
![u=\frac{3}{6}=\frac{1}{2}](https://tex.z-dn.net/?f=u%3D%5Cfrac%7B3%7D%7B6%7D%3D%5Cfrac%7B1%7D%7B2%7D)
Therefore, 1/2 of the tub was used after 6 1/2 hours.
To find the average hourly change, we will put the amount used <em>over</em> the amount of hours. 6 and 1/2 hours is the same as 13/2 hours. Therefore, the hourly change will be:
![c=\frac{\frac{1}{2}}{\frac{13}{2}}](https://tex.z-dn.net/?f=c%3D%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%7D%7B%5Cfrac%7B13%7D%7B2%7D%7D)
Remember when dividing fractions, we:
1) Flip the divisor (the second number).
2) Change the division sign to a multiplication sign.
3) Multiply.
So:
![c=\frac{1}{2}\div\frac{13}{2}\\\Rightarrow c=\frac{1}{2}\times \frac{2}{13}](https://tex.z-dn.net/?f=c%3D%5Cfrac%7B1%7D%7B2%7D%5Cdiv%5Cfrac%7B13%7D%7B2%7D%5C%5C%5CRightarrow%20c%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%5Cfrac%7B2%7D%7B13%7D)
Multiply straight across and reduce:
![c=\frac{2}{26}=\frac{1}{13}](https://tex.z-dn.net/?f=c%3D%5Cfrac%7B2%7D%7B26%7D%3D%5Cfrac%7B1%7D%7B13%7D)
However, since we are <em>using up</em> the tub, our rate will be negative. Therefore:
![c=-\frac{1}{13}](https://tex.z-dn.net/?f=c%3D-%5Cfrac%7B1%7D%7B13%7D)
Therefore, the average hourly rate was -1/13 tub per hour.
This means that after each hour, 1/13 of the tub will be used up.
Edit: Corrected Wrong Answer