Ice cream shop

Jenna works in an ice cream shop. When she starts her shift, the tub of chocolate ice cream is 2/3 full. When she finishes her shift 6 1/2 hours later, there is only 1/6 of the tub left. What was the average hourly change in tub fullness?

Final Answer:

r =  -1/13

Step-by-step explanation:

$$\begin{gathered} a=\frac{2}{3}\doteq 0.6667 \\ b=\frac{1}{6}\doteq 0.1667 \\ \Delta t=6\frac{1}{2}=6+\frac{1}{2}=\frac{6\cdot 2+1}{2}=\frac{12+1}{2}=\frac{13}{2}=6\frac{1}{2}=6.5\text{h} \\ \Delta x=b-a=\frac{1}{6}-\frac{2}{3}=\frac{1}{6}-\frac{4}{6}=\frac{1-4}{6}=\frac{-3}{6}=-\frac{1}{2}=-0.5 \\ r=\frac{\Delta x}{\Delta t}=\frac{\frac{-1}{2}}{\frac{13}{2}}=-\frac{1}{13}=-0.0769 \end{gathered}$$

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