The U.S.S. Carlton comes onto the screen on the lower edge at $200$ mm. The U.S.S. Schmidt enters the screen on the left edge at $200$ mm. At a time $1$ minute later, each ship has moved to a new location. The U.S.S. Carlton has gone $5$ mm North and $2$ mm East of its previous position. The U.S.S. Schmidt has moved $20$ mm East and $5$ mm North of its previous position. Will these two ships collide if they maintain their speeds and directions? If not, how close do they actually come to each other?
First, I solved for parametric equations for both ships:
$\begin{align}\text{USS Carlton - }&x(t)= 200+2t \\ \text{USS Carlton - }&y(t) = 5t\\ \text{Schmidt - }&x(t) = 20t\\ \text{Schmidt - }&y(t) = 200+5t\end{align}$
Next I turned these into regular rectangular equations these being:
$\begin{align}\text{Carlton - }&y= 2.5x-500 \\ \text{Schmidt - }&y=\frac14x +200\end{align}$
These numbers are correct as I have checked them with the answer booklet. Now, I must find if these two ships collide. I do not know how to do this, but I do know how to find the Point of Intersection. To find POI I set the two equations equal to eachother. The POI I got was $(311.11,277.78)$ This is all I know how to do. Please, push me in the right direction. Thank you