A cyclist leaves their home for a $3$-hour ride to a park on a Saturday morning at $8$ A.M. The park is $9$ miles away from their home. On a Monday morning, they cycle back home from the park, starting at $8$ A.M. and taking the same $3$ hours. Let $p\left(t\right)$ be the cyclist's distance from home $t$ hours after $8$ A.M. on Saturday, and $q\left(t\right)$ be the distance from home $t$ hours after $8$ A.M. on Monday. If $r\left(t\right)=p\left(t\right)-q\left(t\right)$, what are $r\left(0\right)$ and $r\left(3\right)$?