Both Taro and Jiro went to Q city from P city by a bicycle.
Taro left P city at 7:00 a.m. and arrived Q city at 10:55 a.m.
Jiro left at 7:30 a.m. and arrived at 10:40 a.m.
Both of them took a rest for 10 minutes only once respectively on the way.
Answer the following questions.
Noted that the speed under run of two bicycles is constant respectively.
(1) Find the ratio of the speed of the bicycle of Taro and of Jiro.
(2) 4 minutes after Taro began to have a rest, Jiro passed Taro.
The time when Jiro passed Taro is considered in two ways.
Find the time respectively.
Answer
(1) 4:5
(2) 9:14 and 10:04
Solution
(1) Calculate the time from P to Q.
Taro : 10:55 - 7:00 = 3 hours 55 minutes
Jiro : 10:40 - 7:30 =3 hours 10 minutes
Find the time which they actually ran by bicycle.
Taro : 3 hours 55 minutes - 10 minutes = 3 hours 45 minutes
Jiro : 3 hours 10 minutes - 10 minutes = 3 hours
The ratio of time taken is Taro : Jiro = 3 hours 45 minutes : 3 hours = 5 : 4
Since the ratio of the speed of Taro and Jiro is the inverse ratio of the ratio of time, then Taro : Jiro = 4 : 5.
(2) There are two cases,
Case1 : Jiro passed Taro before Jiro rest.
Case2 : Jiro passed after he rest.
Case1 : The ratio of the time concerning Taro and Jiro going to the Taro’s rest spot is 5:4.
The time difference concerning actually going to the Taro’s rest spot is 7:30 - 7:00 - 4 minutes = 26 minutes.
The difference of the ratio of the time as 5 - 4 = 1 is corresponding to the actual time of 26 minutes.
The actual time taken by Jiro is 26 minute × 4 = 104 minutes.
Therefore, the time to be found is 7:30. + 104 minutes = 9:14.
Case2 : It is considered that Jiro left at 7:40 and did not take a rest on the way.
The ratio of the time concerning Taro and Jiro going to the Taro’s rest spot is 5:4 as sames as Case1.
The time difference concerning actually going to the Taro’s rest spot is 7:40 - 7:00 - 4 minutes = 36 minutes.
The difference of the ratio of the time as 5 - 4 = 1 is corresponding to the actual time of 36 minutes.
The actual time taken by Jiro is 36 minute × 4 = 144 minutes.
Therefore, the time to be found is 7:40 + 144 minutes = 10:04.
Taro left P city at 7:00 a.m. and arrived Q city at 10:55 a.m.
Jiro left at 7:30 a.m. and arrived at 10:40 a.m.
Both of them took a rest for 10 minutes only once respectively on the way.
Answer the following questions.
Noted that the speed under run of two bicycles is constant respectively.
(1) Find the ratio of the speed of the bicycle of Taro and of Jiro.
(2) 4 minutes after Taro began to have a rest, Jiro passed Taro.
The time when Jiro passed Taro is considered in two ways.
Find the time respectively.
Answer
(1) 4:5
(2) 9:14 and 10:04
Solution
(1) Calculate the time from P to Q.
Taro : 10:55 - 7:00 = 3 hours 55 minutes
Jiro : 10:40 - 7:30 =3 hours 10 minutes
Find the time which they actually ran by bicycle.
Taro : 3 hours 55 minutes - 10 minutes = 3 hours 45 minutes
Jiro : 3 hours 10 minutes - 10 minutes = 3 hours
The ratio of time taken is Taro : Jiro = 3 hours 45 minutes : 3 hours = 5 : 4
Since the ratio of the speed of Taro and Jiro is the inverse ratio of the ratio of time, then Taro : Jiro = 4 : 5.
(2) There are two cases,
Case1 : Jiro passed Taro before Jiro rest.
Case2 : Jiro passed after he rest.
Case1 : The ratio of the time concerning Taro and Jiro going to the Taro’s rest spot is 5:4.
The time difference concerning actually going to the Taro’s rest spot is 7:30 - 7:00 - 4 minutes = 26 minutes.
The difference of the ratio of the time as 5 - 4 = 1 is corresponding to the actual time of 26 minutes.
The actual time taken by Jiro is 26 minute × 4 = 104 minutes.
Therefore, the time to be found is 7:30. + 104 minutes = 9:14.
Case2 : It is considered that Jiro left at 7:40 and did not take a rest on the way.
The ratio of the time concerning Taro and Jiro going to the Taro’s rest spot is 5:4 as sames as Case1.
The time difference concerning actually going to the Taro’s rest spot is 7:40 - 7:00 - 4 minutes = 36 minutes.
The difference of the ratio of the time as 5 - 4 = 1 is corresponding to the actual time of 36 minutes.
The actual time taken by Jiro is 36 minute × 4 = 144 minutes.
Therefore, the time to be found is 7:40 + 144 minutes = 10:04.
