1. The express train is 70 meters long and the local train is 80 meters long. If two cars are driving in the same direction, it takes 20 seconds for the express train to catch up with the local train and leave completely. If two cars drive in the opposite direction, it takes four seconds for the two cars to meet and leave. How many meters per second do you want each car to travel?

Let the express train Xm/s per second and the local train Ym/s per second. Then:

4(X+Y)= 150

20X-20Y= 150

Solution: X = 22.5m m/s

Y= 15m/s

A: The express train is 22.5m/s per second and the local train is 15m/s per second.

2. In the plane rectangular coordinate system, point A (4,0) and point B (0,3) are known. Point P starts from point A and moves to the right at a speed of 1 unit per second, while point Q starts from point B and moves to the right at a speed of 2 units per second, and points P and Q start at the same time.

Add AQ, and when △ABQ is a right triangle, find the coordinates of point Q;

When P and Q move to a certain position, if they are folded along the straight line AQ, the point P just falls on the AB line, and then find the degree of ∠AQP;

(3) The intersection point A is AC⊥AB, the AC intersecting ray PQ is at point C, connecting BC, and D is the midpoint of BC. During the movement of points P and Q, is there a moment that makes a quadrilateral with vertices A, C, Q and D a parallelogram? If so, try to find the value at this time. If it does not exist, please explain why.

I believe you know all the steps (1(2)). (3) When point C is on line PQ, extend the extension line of BQ and AC to point F,

* ac⊥ab

∴ ..................( 1 min)

∫DQ‖AC, DQ=AC, and d is the midpoint of BC.

∴ FC = 2dq = 2ac ................. (1min)

∴

In Rt△BAC, = 4................( 1).

When point c is on the extension line of PQ, the intersection of BQ and AC is f, and the intersection of AD and BQ is g,

∫CQ‖ AD, CQ = AD, and D is the midpoint of BC.

∴ AD=CQ=2DG

∴ CQ=2AG=2PQ

∴ FC=2AF

∴ ……

In Rt△BAC,