① This problem should be discussed in two situations: ① parallelogram APQB, where BQ=AP, ② parallelogram CQ = PD；; , where CQ = PD；;

② The lengths of CQ, BQ, AP and PD are expressed by time t, and then the value of t is obtained according to the above equivalence relation.

explain

Solution:

Let the time of P and Q motion be t(s).

According to the meaning of the question:

CQ=2t，BQ=6-2t，AP=t，PD=9-t

∫ AD ∨ BC

∴

① when BQ=AP

The quadrilateral APQB is a parallelogram.

That is 6-2t = t.

Solution:

t=2

② When CQ=PD.

Quadrilateral CQPD is a parallelogram.

That is 2t = 9t.

Solution:

t = 3；

So when 2 or 3 seconds, the straight line QP cuts the quadrilateral into a parallelogram.