Running in a ring with a length of 150, the distance between upper and lower armor is 75 meters, and the distance between armor and lower armor is 30 meters. Armour A, Armour A, Armour A and Armour B run at the speed of 7 meters, 2 meters and 4 meters per second respectively. How many seconds will it take them to meet? (Hint: If the distance difference of several people is not considered at first, the first meeting time of three people is 150s.)

Analysis: ∵ A is 75 meters away from B and B is 30 meters away from C, but the title does not explain the mutual position of the three people at the starting point, so it is necessary to discuss the mutual position of the three people. From the mutual position of Serie A, B and C, there are two possibilities:

(1) A is at the end, B is in the middle and C is in the front;

(2) A is at the end, C is in the middle and B is in the front;

(1) Analysis: ∵ The length of circular track is 150, the distance between A and B is 75m, and the distance between B and C is 30m. A, B and C run at the speed of V 1=7m, V2=2m and V3=4m per second respectively.

Let the meeting time be T. At the beginning, A comes last, B is in the middle and C is in the front.

The distance between Party A and Party B is 75, and that between Party A and Party C is 105.

7t/ 150 (take the remainder) =(2t+75)/ 150 (take the remainder) =(4t+ 105)/ 150 (take the remainder).

When t= 135, the above formula holds.

(2) Analysis: When starting, A is at the end, C is in the middle, and B is in front.

The distance between a and b is 75, and the distance between a and c is 45.

7t/ 150 (take the remainder) =(4t+45)/ 150 (take the remainder) =(2t+75)/ 150 (take the remainder).

When t= 15, the above formula holds.