$36 \cdot 38$ As shown, in rectangle $ABCD$, $AB=4 \text{ cm}, AD=12 \text{ cm}$. Point $P$ is on $AD$, moving from $A$ to $D$ at a speed of $1 \text{ cm}$ per second; point $Q$ is on $BC$, moving from $C$ at a speed of $3 \text{ cm}$ per second, back and forth between $C$ and $B$. Both points start at the same time, until point $P$ reaches point $D$. During this time, the number of times line segment $PQ$ is parallel to $AB$ is
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(9th "Jinyun Cup" Junior High School Mathematics Invitational Competition, 1992)
[Solution] Let $M, N$ be the trisection points of $A D$.
When point $P$ moves from $A$ to $M$, point $Q$ moves from $C$ to $B$, and at some moment during this process, line segment $P Q$ is parallel to $A B$ once.

Similarly, when point $P$ moves from $M$ to $N$, or from $N$ to $D$, at some moment during each of these processes, line segment $P Q$ is parallel to $A B$ once.
Therefore, as $P$ moves from $A$ to $D$, $P Q$ is parallel to $A B$ three times. Hence, the answer is (C).