The way from the house of Taro and Jiro to the school joins at the point A, as shown in a figure.
As for the distance to A point, Taro’s house is more 750 m far than Jiro’s house.
Moreover, it is 1000 m from A point up to the school.
Usually, Taro leaves home at 7:50 in the morning, goes at 100 m/m to school and reaches 5 minutes before the starting time.
Usually, Jiro passes along A point 7 minutes later than Taro and reaches exactly at the starting time.
Since it was 5 minutes late to leave home today, Jiro ran at the twice the speed of usual.
Jiro caught up with Taro at the middle point between A point and school.
Answer the following questions.
(1) Find the speed at which Jiro usually walks.
(2) Find the time delayed Jiro passed through A point than Taro today.
(3) Find the distance between Jiro’s house and A point.
(4) Find the starting time of the school.
Answer
(1) 125 m per minute
(2) 3 minutes
(3) 2250 m
(4) 8:35
Solution
(1) When Jiro reaches A point, the time lag with Taro is 7 minutes.
Taro arrives at school 5 minutes before the starting time and Jiro arrives at the starting time.
It turns out that the time lag with Taro comes to 5 minutes when Jiro arrives at school.
The time lag is shortened 7 minute - 5 minute = 2 minute.
Taro moved from A point to the school 1000/100 = 10 minutes.
Thus, Jiro takes 10 minutes - 2 minutes = 8 minutes.
Therefore, the speed per minute of Jiro is 1000 / 8= 125 m.
(2) The speed per minute of today's Jiro is 125 × 2=250m.
The distance from A point to the halfway point is 500 m.
Taro moves this distance in 500 / 250 = 2 minutes and Jiro moves in 500 / 100 = 5 minutes.
Therefore, the delay in A point is 5 minutes to 2 minute = 3 minutes.
(3) When Jiro passed along the A point, he was usually late for Taro for 7 minutes, but it was for 3 minutes today.
This means that today it was 4 minutes earlier than usual.
Moreover, since it was 5 minutes later than usual that Jiro left home, it turns out that he ran from his house to A point for 4 + 5 = 9 minutes earlier today.
As shown in Fig. 1, since it is twice the usual speed today, the time ratio becomes 2 : 1.
The difference of the time ratio 2 - 1 =1 is equivalent to 9 minutes.
Since the time taken today is 1 as time ratio, actual time is 9 minutes.
Therefore, the distance from the house of Jiro to A point is 250m/m × 9 minutes = 2250m.
(4) Since Taro’s house is located 750 m further than Jiro’s house, the distance from Taro’s house to the school is 750 + 2250 + 1000 = 4000m.
Since Taro’s speed is 100 m/m, it takes 4000 / 100 = 40 minutes from the house to the school.
Since Taro leaves home at 7:50, he arrives at school at 7:50 + 40 minute = 8:30.
Since this time is 5 minutes before the starting time, the starting time is at 8:30 + 5 minute = 8:35.
As for the distance to A point, Taro’s house is more 750 m far than Jiro’s house.
Moreover, it is 1000 m from A point up to the school.
Usually, Taro leaves home at 7:50 in the morning, goes at 100 m/m to school and reaches 5 minutes before the starting time.
Usually, Jiro passes along A point 7 minutes later than Taro and reaches exactly at the starting time.
Since it was 5 minutes late to leave home today, Jiro ran at the twice the speed of usual.
Jiro caught up with Taro at the middle point between A point and school.
Answer the following questions.
(1) Find the speed at which Jiro usually walks.
(2) Find the time delayed Jiro passed through A point than Taro today.
(3) Find the distance between Jiro’s house and A point.
(4) Find the starting time of the school.
Answer
(1) 125 m per minute
(2) 3 minutes
(3) 2250 m
(4) 8:35
Solution
(1) When Jiro reaches A point, the time lag with Taro is 7 minutes.
Taro arrives at school 5 minutes before the starting time and Jiro arrives at the starting time.
It turns out that the time lag with Taro comes to 5 minutes when Jiro arrives at school.
The time lag is shortened 7 minute - 5 minute = 2 minute.
Taro moved from A point to the school 1000/100 = 10 minutes.
Thus, Jiro takes 10 minutes - 2 minutes = 8 minutes.
Therefore, the speed per minute of Jiro is 1000 / 8= 125 m.
(2) The speed per minute of today's Jiro is 125 × 2=250m.
The distance from A point to the halfway point is 500 m.
Taro moves this distance in 500 / 250 = 2 minutes and Jiro moves in 500 / 100 = 5 minutes.
Therefore, the delay in A point is 5 minutes to 2 minute = 3 minutes.
(3) When Jiro passed along the A point, he was usually late for Taro for 7 minutes, but it was for 3 minutes today.
This means that today it was 4 minutes earlier than usual.
Moreover, since it was 5 minutes later than usual that Jiro left home, it turns out that he ran from his house to A point for 4 + 5 = 9 minutes earlier today.
As shown in Fig. 1, since it is twice the usual speed today, the time ratio becomes 2 : 1.
The difference of the time ratio 2 - 1 =1 is equivalent to 9 minutes.
Since the time taken today is 1 as time ratio, actual time is 9 minutes.
Therefore, the distance from the house of Jiro to A point is 250m/m × 9 minutes = 2250m.
(4) Since Taro’s house is located 750 m further than Jiro’s house, the distance from Taro’s house to the school is 750 + 2250 + 1000 = 4000m.
Since Taro’s speed is 100 m/m, it takes 4000 / 100 = 40 minutes from the house to the school.
Since Taro leaves home at 7:50, he arrives at school at 7:50 + 40 minute = 8:30.
Since this time is 5 minutes before the starting time, the starting time is at 8:30 + 5 minute = 8:35.
