The first case: there is no C at two points.

AP=2t，BQ=3t

CP=AC-AP=6-2t

CQ=BC-BQ=8-3t

It is easy to prove that two triangles are similar. If CP=CQ, then these two triangles are congruent.

6-2t=8-3t

t=2

The second case: p and q coincide.

CP=6-2t

CQ=3t-8

6-2t=3t-8

t=2.8

The third case: Q goes to A, and P doesn't go to B (because Q runs fast, when P passes C, Q has already run more 1/3, so it can't be expressed.

2t-6=3t-8)

CP=2t-6=AC=6

t=6

So there are three solutions to this problem: 2 2.8 6.

Answer over