A, B and C are in the surroundings of a circular pond as shown in a figure at equal intervals.
They began to run at the same time in the direction of the arrow in a figure respectively with the same speed.
When two of three persons meet, the two persons run with the speed same for opposite.
Three person’s speed is 150 m/m.
Answer the following questions.
(2) Find the time for three persons to return the original position at the same time from the start.
Moreover, find the sum total number of times with which two of three persons meet in the time.
Fig.2 shows the motion of three persons until the first meeting of A and B.
Fig.3 shows the motion of three persons until the next meeting of A and C who meet at point 1.
Fig. 5 shows three persons' motion for 24 minutes.
According to this graph, it turns out that a motion of B for 12 minute ~ 24 minutes is the same as a motion of C for 0 minute ~ 12 minutes.
A motion of A and B can be also said the same thing.
Furthermore, A, B, and C are in the original position of B, C, and A in 12 minutes, respectively.
When it is expressed as (A, B, C) → (B, C, A), it turns out that it becomes (A, B, C) → (B, C, A) → (C, A, B) in 24 minutes.
Based on the above,the time concerning A, B, and C returning to the first position is 12 minute × 3 = 36 minutes.
Moreover, according to Fig. 5, it is 4 times that two of three persons have met in 12 minutes.
Then, in 36 minutes, the number of times is 4 times × 3= 12 times.
They began to run at the same time in the direction of the arrow in a figure respectively with the same speed.
When two of three persons meet, the two persons run with the speed same for opposite.
Three person’s speed is 150 m/m.
Answer the following questions.
(1) It took 10 minutes for A to meet B 2nd time from the start.
Find the length of a round of the pond.
(2) Find the time for three persons to return the original position at the same time from the start.
Moreover, find the sum total number of times with which two of three persons meet in the time.
Answer
Solution
(1) It is in the middle between original position of A and B that A and B meet for the first time.
Thus, the circumference is divided into six equal parts as shown in Fig.1.
(1) 1800 m
(2) 36 minutes, 12 times
(2) 36 minutes, 12 times
(1) It is in the middle between original position of A and B that A and B meet for the first time.
Thus, the circumference is divided into six equal parts as shown in Fig.1.
The original positions of A, B, and C are 1, 3, and 5, respectively.
Fig.2 shows the motion of three persons until the first meeting of A and B.
Fig.3 shows the motion of three persons until the next meeting of A and C who meet at point 1.
Fig. 4 shows the motion of three persons until the second meeting of A and B.
A moved five parts of six parts of the divided circumference as point 1-2-1-2-3-4 for 10 minutes until the second meeting with B.
The distance which A moved is 150 m/m × 10 minute = 1500 m.
Therefore, the length of the circumference is 1500 m / 5 × 6 = 1800 m.
The distance which A moved is 150 m/m × 10 minute = 1500 m.
Therefore, the length of the circumference is 1500 m / 5 × 6 = 1800 m.
(2) Since it is 10 minutes with five scales in horizontal scale in Fig. 4, it is 2 minutes with one scale.
Fig. 5 shows three persons' motion for 24 minutes.
According to this graph, it turns out that a motion of B for 12 minute ~ 24 minutes is the same as a motion of C for 0 minute ~ 12 minutes.
A motion of A and B can be also said the same thing.
Furthermore, A, B, and C are in the original position of B, C, and A in 12 minutes, respectively.
When it is expressed as (A, B, C) → (B, C, A), it turns out that it becomes (A, B, C) → (B, C, A) → (C, A, B) in 24 minutes.
Based on the above,the time concerning A, B, and C returning to the first position is 12 minute × 3 = 36 minutes.
Moreover, according to Fig. 5, it is 4 times that two of three persons have met in 12 minutes.
Then, in 36 minutes, the number of times is 4 times × 3= 12 times.
