Answer:
[tex]-1/13\text{ tub per hour}[/tex]
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:
[tex]u=\frac{2}{3}-\frac{1}{6}[/tex]
Make a common denominator. Change 2/3 to 4/6 by multiplying both layers by 2. So:
[tex]u=\frac{4}{6}-\frac{1}{6}[/tex]
Subtract and reduce:
[tex]u=\frac{3}{6}=\frac{1}{2}[/tex]
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 over the amount of hours. 6 and 1/2 hours is the same as 13/2 hours. Therefore, the hourly change will be:
[tex]c=\frac{\frac{1}{2}}{\frac{13}{2}}[/tex]
Remember when dividing fractions, we:
1) Flip the divisor (the second number).
2) Change the division sign to a multiplication sign.
3) Multiply.
So:
[tex]c=\frac{1}{2}\div\frac{13}{2}\\\Rightarrow c=\frac{1}{2}\times \frac{2}{13}[/tex]
Multiply straight across and reduce:
[tex]c=\frac{2}{26}=\frac{1}{13}[/tex]
However, since we are using up the tub, our rate will be negative. Therefore:
[tex]c=-\frac{1}{13}[/tex]
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
