Taro and Jiro are going back and forth between A point and B point with a fixed speed respectively by the bicycle.
They turn up immediately at A point and B point without taking a rest.
Taro started from A point and Jiro started from B point at the same time.
They passed at the point of 7 km from A first.
They move forward and they passed 2nd time at the point of 6 km from B.
Answer the following questions.
(1) In case Taro is faster than Jiro, find the speed ratio of Taro and Jiro.
(2) In case Jiro is faster than Taro, find the speed ratio of Taro and Jiro.
Noted that if there are some answers to this question, answer all cases.
They turn up immediately at A point and B point without taking a rest.
Taro started from A point and Jiro started from B point at the same time.
They passed at the point of 7 km from A first.
They move forward and they passed 2nd time at the point of 6 km from B.
Answer the following questions.
(1) In case Taro is faster than Jiro, find the speed ratio of Taro and Jiro.
(2) In case Jiro is faster than Taro, find the speed ratio of Taro and Jiro.
Noted that if there are some answers to this question, answer all cases.
Answer
Fig. 1 expresses the 1st meeting.
The situation of the 2nd meeting is considered in Fig.2, Taro moves 7 km × 2= 14 km.
In this figure, it means that Jiro had moved 8 km at the time of the 1st meeting.
Since Jiro is faster than Taro, it does not suit to the condition that Taro is faster than Jiro.
As shown in Fig. 3 instead of Fig. 2, it turns out that Taro moved very fast.
In this case, the distance Taro moved at the time of 2nd meeting is 7 km + 14 km = 21 km.
The distance Jiro moved is 6 km.
Therefore, the ratio of the speed of Taro and Jiro is equal to the ratio of the distance they moved, it is 21km : 6km = 7 : 2.
(2) Since Jiro is faster than Taro in the case of Fig. 2, this case is suitable to the condition of (2) and the speed ratio is Taro : Jiro = 7 : 8.
As for another case, Fig. 4 can be considered.
A distance moved by the 2nd meeting from the 1st meeting is found from this figure.
The distance Taro moved is 14 km and Jiro is 7 + 27 + 6 = 40 km.
Therefore, the speed ratio is Taro : Jiro = 14 : 40 = 7 : 20.
(1) Taro : Jiro = 7 : 2
(2) Taro : Jiro = 7 : 8, 7 : 20
(2) Taro : Jiro = 7 : 8, 7 : 20
Solution
(1) The sum of distance which two persons moved by the 2nd meeting from the first meeting is twice the sum of distance of the 1st time.
Fig. 1 expresses the 1st meeting.
Taro moved 7 km at the time of the 1st meeting.
The situation of the 2nd meeting is considered in Fig.2, Taro moves 7 km × 2= 14 km.
In this figure, it means that Jiro had moved 8 km at the time of the 1st meeting.
Since Jiro is faster than Taro, it does not suit to the condition that Taro is faster than Jiro.
As shown in Fig. 3 instead of Fig. 2, it turns out that Taro moved very fast.
In this case, the distance Taro moved at the time of 2nd meeting is 7 km + 14 km = 21 km.
The distance Jiro moved is 6 km.
Therefore, the ratio of the speed of Taro and Jiro is equal to the ratio of the distance they moved, it is 21km : 6km = 7 : 2.
(2) Since Jiro is faster than Taro in the case of Fig. 2, this case is suitable to the condition of (2) and the speed ratio is Taro : Jiro = 7 : 8.
As for another case, Fig. 4 can be considered.
A distance moved by the 2nd meeting from the 1st meeting is found from this figure.
The distance Taro moved is 14 km and Jiro is 7 + 27 + 6 = 40 km.
Therefore, the speed ratio is Taro : Jiro = 14 : 40 = 7 : 20.
