\begin{frame}
  \frametitle{Related (Dependent) Rates}

  \begin{exampleblock}{}
    Two cars are headed for the same road intersection:
    \begin{itemize}
      \item car $A$ is traveling west with $50$mi/h
      \item car $B$ is traveling north with $60$mi/h
    \end{itemize}
    At what rate are the cars approaching \\
    when $A$ is $0.3$mi and $B$ is $0.4$mi
    from the intersection?
    \medskip
    
    \begin{minipage}{.39\textwidth}
    \begin{center}
      \begin{tikzpicture}[default]
        \draw (-0.3,0) -- node[pos=.4,above] {$\mpause[1]{x}$} (3,0);
        \draw (0,.3) -- node[pos=.4,left] {$\mpause[2]{y}$} (0,-2.3);
        \node at(0,0) [anchor=south east] {$C$};
        \begin{scope}[cred]
        \draw[dashed] (0,-1.5) -- node[below,anchor=north west] {$\mpause[3]{z}$} node [at start,left] {$B$} node [at end,above] {$A$} (2,0);
        \end{scope}
%         \begin{scope}
%         \mpause[4]{
%           \draw[->] (2.3,.5) -- node [above] {$\frac{d}{dt}x = -50$} ++(-.6,0);
%         }
%         \mpause[5]{
%           \draw[->] (-.5,-1.8) -- node [left] {$\frac{d}{dt}y = -60$} ++(0,.6);
%         }
%         \end{scope}
      \end{tikzpicture}
    \end{center}
    \end{minipage}
    \begin{minipage}{.59\textwidth}
      \begin{itemize}
      \pause
        \item $x(t) =$ distance of $A$ to crossing
      \pause
        \item $y(t) =$ distance of $B$ to crossing
      \pause
        \item $z(t) =$ distance of $A$ to $B$
      \end{itemize}
      \pause
      \begin{malign}
        \frac{d}{dt}x = -50 && \frac{d}{dt}y = -60
      \end{malign}
    \end{minipage}
    \pause
    \begin{talign}
      &z^2 = x^2 + y^2
%       \mpause[1]{\;\implies\; \frac{d}{dt}z^2 = \frac{d}{dt} (x^2 + y^2)}\\
      \mpause[1]{\;\implies\; 2z\frac{dz}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}}\\
      &\mpause[2]{\frac{dz}{dt} = \frac{x}{z}\frac{dx}{dt} + \frac{y}{z}\frac{dy}{dt}}
      \mpause[5]{\implies\; \frac{dz}{dt} = \frac{0.3}{0.5}(-50) + \frac{0.4}{0.5}(-60)}
      \mpause[6]{=-78}
    \end{talign}
    \pause\pause\pause
    When $x = 0.3$ \& $y = 0.4$, we get $z = \pause 0.5$.
    \pause\pause\pause
    The answer is \alert{$78$mi/h}.
  \end{exampleblock}  
\end{frame}