Three points moving on a rectangle

As shown in Fig. 1, there is a rectangle ABCD whose length of side AB is 18 cm and length of side AD is 42 cm.

The point P leaves A and moves at the speed of 3 cm/s clockwise rotation on the side of rectangle ABCD as A -> D -> C -> B -> A.

It will stop when it arrives at A again.

The point Q leaves B at the same time as P leaves A.

It moves counterclockwise until P stops at the speed of 2 cm/s on the side of rectangle.

Answer the following questions.

(1) In how many seconds after started is it that P and Q meet?

(2) The point R leaves A at the same time with P and moves counterclockwise on the side of the rectangle at the speed of 2 cm/s.

It moves until P stops.

The figure which connected three point P, Q, and R is considered.

(2)-1 A triangle is not made several times while three points are moving.

Find the time altogether when the triangle is not be made.

The time should be found the time since they begin to move.

For example, When the triangle is not be made all the time from x-second to y-second, you may answer as x~y seconds.

(2)-2 As shown in Fig. 2, the intersection of the line AC and the line BD is set to E.

Find the time altogether when E is on the inside and circumference of the triangle PQR.

In accordance with (2)-1, answer the time altogether.

Answer