An express train goes from A to B, and a local train goes from B to A. Both cars start at the same time. Let the local train travel as x(h) and the distance between two cars as y(km). The dotted line in the figure represents the functional relationship between y and x, and answers the following questions according to the image:

(1) The distance between Party A and Party B is _ _ _ _ _ _ _ _ km.

(2) The actual meaning of point B in the figure is _ _ _ _ _ _ _ _ _ _ _ _;

(3) Find the speed of the local train and the express train;

(4) Find the functional relationship between Y and X represented by BC line, and write the range of independent variable X;

(5) If the second express also goes from A to B, the speed is the same as that of the first express. Thirty minutes after the first express train meets the local train, the second express train meets the local train. How many hours does it leave after the first express?

Solution: (1) 900;

(2) The practical significance of point B in the figure is that when the local train runs for 4 hours, the local train meets the express train.

(3) According to the image, the traveling distance of the local train 12h is 900km.

So the speed of the local train = 75 (km/h);

When the local train runs for 4 hours, the local train and the express train meet, and the sum of the driving distances of the two cars is 900km. ..

So the sum of the speeds of the local train and the express train = 225 (km/h), so the speed of the express train is 150 (km/h).

(4) According to the meaning of the question, the express train travels 900km to reach B, so the express train travels = 6 (h) to reach B, and the distance between the two cars is 6× 75 = 450 (km).

So the coordinate of point C is (6450).

Let the functional relationship between y and x represented by the straight line BC be y = kx+b,

Replace with (4,0) and (6,450).

So the functional relationship between y and x represented by BC line is y = 225 x-900.

The range of independent variable x is 4 ≤ x ≤ 6. (8 points)

(5) After 30 minutes, the local train meets the first express train and the second express train. At this time, the running time of the local train is 4.5 hours.

Substitute x = 4.5 into y = 225x-900 to get y = 1 12.5.

At this time, the distance between the local train and the first express train is equal to the distance between the two express trains, which is 1 12.5km.

So the interval between the two express trains is112.5÷150 = 0.75 (h).

That is, the second express train leaves 0.75 hours later than the first express train.