\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} The position of particle $P$ at time
$t$ is given by $\cases{x=t&\cr y=2t-1&\cr}$ and the position of
particle $Q$ at time $t$ is given by $\cases{x=3t-t^2&\cr y=t+1&\cr}$.

\medskip

\noindent a) Sketch both paths as well as possible. Be sure to label
the paths with the particles ($P$ and $Q$) traveling on each of them.

\medskip

\noindent b) Find the \underbar{two} points of intersection of the
paths exactly using algebra.  

\medskip

\noindent c) Do the particles ever collide? You should support your
answer (one of ${\bf \{Yes|No\}}$) with some reason.

\vfil\eject\end