Answer
The required solution is $\text{157}\ \text{ft/min}$
Work Step by Step
The angle covered in one revolution is $2\pi \ \text{radians}$.
The carousel is rotating at 2.5 revolutions per minute.
The angle covered in one minute is
$2.5\left( 2\pi \ \text{radians} \right)=5\pi \ \text{radians}$
Angular speed $\omega $ is $5\pi \ \text{radians per minute}$.
And the outer row of the animals is $20\ \text{feet}$ from the center denoted by ${{r}_{1}}$.
The linear speed ${{v}_{1}}$ of the outer row of animals is given by
${{v}_{1}}={{r}_{1}}\omega $
Put $20\ \text{feet}$ for ${{r}_{1}}$ and $5\pi \ \text{radians per minute}$ for $\omega $:
$\begin{align}
& {{v}_{1}}=\left( 20\ \text{feet} \right)\left( 5\pi \ \text{radians per minute} \right) \\
& =100\pi \ \text{feet per minute}
\end{align}$
The inner row of animals is $10\ \text{feet}$ from the center denoted by ${{r}_{2}}$.
The linear speed ${{v}_{2}}$ of the inner row of animals is given by
${{v}_{2}}={{r}_{2}}\omega $
put $10\ \text{feet}$ for ${{r}_{2}}$ and $5\pi \ \text{radians per minute}$ for $\omega $:
$\begin{align}
& {{v}_{2}}=\left( 10\ \text{feet} \right)\left( 5\pi \ \text{radians per minute} \right) \\
& =50\pi \ \text{feet per minute}
\end{align}$
And the difference in linear speeds of outer and inner row of animals is given by
$\Delta v={{v}_{1}}-{{v}_{2}}$
Put $100\pi \ \text{feet per minute}$ for ${{v}_{1}}$ and $50\pi \ \text{feet per minute}$ for ${{v}_{2}}$:
$\begin{align}
& \Delta v=100\pi \ \text{feet per minute}-50\pi \ \text{feet per minute} \\
& =50\pi \ \text{feet per minute}
\end{align}$
Put $\pi =3.14159$:
$\begin{align}
& \Delta v=50\left( 3.14159 \right)\ \text{feet per minute} \\
& =\text{157}\text{.07}\ \text{feet per minute}\approx \text{157}\ \text{feet per minute}
\end{align}$
