Taro walks around a certain pond with fixed speed and Jiro runs with fixed speed to opposite direction.
Taro passed by Jiro again 10 minutes after passing by Jiro.
Just after first passing, Taro also started running increasing the speed by 120 m/m more than the speed at walking.
Then he passed by Jiro 6 minutes afterward again.
Answer the following questions.
(1) Find the surrounding length of the pond.
(2) After passing first, in order to pass again in 4 minutes and 48 seconds, find the speed per minute which Taro increases from the speed at walking first.
(3) If Taro runs with speed twice the speed of walking first after passing first, he will pass again in 7 minutes and 12 seconds.
Find the speed per minute of Jiro.
Answer
(1) 1800 m
(2) 195 m/m
(3) 110 m/m
Solution
(1) Set the surrounding length of a pond to 30 of the least common multiple of 6 and 10.
The sum total of two persons' speed when it passes first is 30 / 10 minutes = 3.
Moreover, the sum total of speed when Taro increases speed 120 m/m is 30 / 6 minutes = 5.
Only Taro increased speed.
Taro passed by Jiro again 10 minutes after passing by Jiro.
Just after first passing, Taro also started running increasing the speed by 120 m/m more than the speed at walking.
Then he passed by Jiro 6 minutes afterward again.
Answer the following questions.
(1) Find the surrounding length of the pond.
(2) After passing first, in order to pass again in 4 minutes and 48 seconds, find the speed per minute which Taro increases from the speed at walking first.
(3) If Taro runs with speed twice the speed of walking first after passing first, he will pass again in 7 minutes and 12 seconds.
Find the speed per minute of Jiro.
Answer
(1) 1800 m
(2) 195 m/m
(3) 110 m/m
Solution
(1) Set the surrounding length of a pond to 30 of the least common multiple of 6 and 10.
The sum total of two persons' speed when it passes first is 30 / 10 minutes = 3.
Moreover, the sum total of speed when Taro increases speed 120 m/m is 30 / 6 minutes = 5.
Only Taro increased speed.
The sum total of two persons' speed increased from 3 to 5 and the difference 2 is equivalent to 120 m/m.
The speed of 3 which is the sum of two persons' first speed is 120 / 2 × 3 = 180m/m.
Therefore, since it took 10 minutes to pass first, the surrounding length of the pond is 180 m/m × 10 minutes = 1800m.
(2) They pass 1800 m in 4 minute 48 second = 24/5 minutes.
The sum total of two persons' speed is 1800 m / (24/5) minutes = 375 m/m.
Since the sum total of two persons' first speed is 180 m/m, the speed which Taro increases is 375 - 180 = 195 m/m.
(3) They pass 1800 m in 7 minute 12 second = 36/5 minutes.
The sum of two persons' speed becomes 1800 m / (36/5)5 minutes = 250 m/m.
Since the sum total of two persons' first speed is 180 m/m, the speed which Taro increases is 250 - 180 = 70 m/m.
Since Taro increased speed twice, the first speed of Taro is also 70 m/m.
Since the sum total of two persons' first speed was 180 m/m, the speed of Jiro is 180 - 70 = 110 m/m.
The speed of 3 which is the sum of two persons' first speed is 120 / 2 × 3 = 180m/m.
Therefore, since it took 10 minutes to pass first, the surrounding length of the pond is 180 m/m × 10 minutes = 1800m.
(2) They pass 1800 m in 4 minute 48 second = 24/5 minutes.
The sum total of two persons' speed is 1800 m / (24/5) minutes = 375 m/m.
Since the sum total of two persons' first speed is 180 m/m, the speed which Taro increases is 375 - 180 = 195 m/m.
(3) They pass 1800 m in 7 minute 12 second = 36/5 minutes.
The sum of two persons' speed becomes 1800 m / (36/5)5 minutes = 250 m/m.
Since the sum total of two persons' first speed is 180 m/m, the speed which Taro increases is 250 - 180 = 70 m/m.
Since Taro increased speed twice, the first speed of Taro is also 70 m/m.
Since the sum total of two persons' first speed was 180 m/m, the speed of Jiro is 180 - 70 = 110 m/m.
