Taro, Jiro and Hanako continue running around the surroundings of a pond with a fixed speed, respectively.
Taro and Jiro run in the same direction and Hanako runs in an opposite direction.
Taro passes Jiro every 15 minutes and Jiro meets with Hanako every 2 minutes.
Hanako runs in 8 minutes the distance where Jiro runs in 7 minutes.
Find the ratio of the speed of Taro and Hanako in this case.
Taro and Jiro run in the same direction and Hanako runs in an opposite direction.
Taro passes Jiro every 15 minutes and Jiro meets with Hanako every 2 minutes.
Hanako runs in 8 minutes the distance where Jiro runs in 7 minutes.
Find the ratio of the speed of Taro and Hanako in this case.
Answer
10：7
Solution
Hanako runs in 8 minutes the distance where Jiro runs in 7 minutes.
The ratio of the time when Jiro and Hanako run the same distance is 7 : 8.
In case the distance is the same, the ratio of speed turns into an inverse ratio of the ratio of the time taken.
The ratio of speed is Jiro : Hanako = 8 : 7.
Moreover, since Jiro and Hanako meet every 2 minutes, a surrounding distance of the pond can be expressed as (8 + 7) × 2 = 30.
Taro passes Jiro every 15 minutes.
The difference of two persons' speed is 30 / 15 = 2.
Since the speed of Jiro is 8, the speed of Taro who faster than Jiro is 8 + 2 = 10.
Therefore, the ratio of the speed of Taro and Hanako is 10 : 7.
