grade.tex

\documentclass[noauthor,nooutcomes,hints,handout]{ximera}

\input{../preamble.tex}

\title{Grade}
\author{Claire Merriman and Bart Snapp}

\begin{document}
\begin{abstract}
  We think about slope and grade.
\end{abstract}
\maketitle

\begin{listOutcomes}
\item Solve a problem where slope is given.
\item Distinguish between slope and grade.
\end{listOutcomes}
\mynewpage

\begin{question}
  The Americans with Disabilities Act (ADA) has special guideline for
  ramps. The ADA says that ramps:
  \begin{itemize}
  \item Should have a slope $1:12$, meaning a rise of $1$ foot for
    every $12$ feet in horizontal length.
  \item The height of each run cannot exceed $30$ inches, though any
    number of runs may be used provided they are separated by rest
    platforms.
  \end{itemize}
  Now for some questions.
\begin{enumerate}
 \item What is the longest a ramp can be in single run?
 \item The grade of the ramp is the slope expressed as a percentage. What is the maximum grade of a ramp?
\end{enumerate}
In each case, show work and explain your reasoning. 

\end{question}

\mynewpage

\begin{question}
The entrance to the Math Tower from 18th Avenue is $7\ stairs$
tall. Each stair is $13\ inches$ long and $5.5\ inches$ tall. If OSU
wanted to add a ramp at this entrance\dots
\begin{enumerate}
\item How many runs would be needed?
\item How long would each run need to be? 
\end{enumerate}
 In each case, show work and explain your reasoning.
\end{question}

\mynewpage

\begin{question}
Roads are typically measured with \textbf{grade}. Grade is simply
turning the slope into a percentage; that is, a slope with a
denominator of $100$.  Here are two road grade warning signs. Each
give a grade and a mileage.
\begin{center}
\includegraphics[width=.4\textwidth]{gradeWarning}
\includegraphics[width=.3\textwidth]{truckGradeWarning}
\end{center}
In each case, find the change in elevation over the warning area. As a
reminder, $1$ mile is $5280$ feet. In each case, show work and explain your reasoning. 

\end{question}

\end{document}