Taro, Jiro and Hanako run in the school grounds of one lap of 360m from a starting line with the constant speed, respectively.
Taro and Jiro run in clockwise and Hanako runs counterclockwise.
When Hanako ran 135m, she met Taro and met Jiro when Hanako ran 25m more.
When Taro was one lap, how long to the starting line is Jiro running ?
Answer
90 m
Solution
Since the ratio of the speed of Taro and Hanako is equal to the ratio of a distance advanced in same time, it is (360 - 135) : 135 = 5 : 3.
The ratio of the speed of Jiro and Hanako is considered the same way, and is (360 - 135 - 25) : (135 + 25) = 5 : 4.
The ratio of three persons' speed is made into a continuous ratio and it will be set to that Taro : Jiro : Hanako = 20 : 15 : 12.
The ratio of the speed of Taro and Jiro is 20 : 15 = 4 : 3.
Therefore, when Taro is one lap, Jiro is 90 m short of the starting line by the calculation of 360 × (4 - 3)/4 = 90.
Taro and Jiro run in clockwise and Hanako runs counterclockwise.
When Hanako ran 135m, she met Taro and met Jiro when Hanako ran 25m more.
When Taro was one lap, how long to the starting line is Jiro running ?
Answer
90 m
Solution
Since the ratio of the speed of Taro and Hanako is equal to the ratio of a distance advanced in same time, it is (360 - 135) : 135 = 5 : 3.
The ratio of the speed of Jiro and Hanako is considered the same way, and is (360 - 135 - 25) : (135 + 25) = 5 : 4.
The ratio of three persons' speed is made into a continuous ratio and it will be set to that Taro : Jiro : Hanako = 20 : 15 : 12.
The ratio of the speed of Taro and Jiro is 20 : 15 = 4 : 3.
Therefore, when Taro is one lap, Jiro is 90 m short of the starting line by the calculation of 360 × (4 - 3)/4 = 90.
