Answer
$1508$ feet/minute
Work Step by Step
The angle covered in one revolution is $2\pi \ \text{radians}$.
The water wheel is rotating at 20 revolutions per minute.
The angle covered in one minute is
$20\left( 2\pi \ \text{radians} \right)=40\pi \ \text{radians}$.
And the angular speed $\omega $ is $40\pi \ \text{radians per minute}$.
The radius of the Ferris wheel $ r $ is $12\ \text{feet}$.
The linear speed $ v $ is given by
$ v=r\omega $
Put $12\ \text{feet}$ for $ r $ and $40\pi \ \text{radians per minute}$ for $\omega $:
$\begin{align}
& v=\left( 12\ \text{feet} \right)\left( 40\pi \ \text{radians per minute} \right) \\
& =480\pi \ \text{feet per minute}
\end{align}$
Put $\pi =3.14159$:
$\begin{align}
& v=480\left( 3.14159 \right)\ \text{feet per minute} \\
& \text{=1507}\text{.96}\ \text{feet}\ \text{per minute}\approx \text{1508 feet}\ \text{per minute}
\end{align}$
