Taro, Jiro, and Hanako move forward from a certain point in the same direction at constant speed respectively.
First, Hanako left at 9:00, Jiro left at 9:06 and Taro left at 9:08, respectively.
Jiro caught up with Hanako at 9:16 and Taro caught up with Hanako at 9:20.
Find the time when Taro catches up with Jiro.
Answer
9: 56
Solution
Since Jiro took 10 minutes and Hanako took 16 minutes to the place where Jiro caught up with Hanako, the ratio of the speed of Hanako and Jiro is an inverse ratio of the ratio of the taken time and it turns out to be 10 : 16 = 5 : 8.
Since Taro took 12 minutes and Hanako took 20 minutes to the place where Taro caught up with Hanako, the ratio of the speed of Hanako and Taro is an inverse ratio of the ratio of the taken time, and it turns out to be 12 : 20 = 3 : 5.
The ratio of three persons' speed is made into a continuous ratio, then it is Taro : Jiro : Hanako = 25 : 24 : 15.
Since Taro moves at the time of 24 and Jiro moves at the time of 25 to the point where Taro catches up with Jiro, 25 - 24 = 1 of the difference of time corresponds in 9:08 to 9:06 = 2 minutes.
Therefore, since the actual time turns out to be 2 minute × 25 = 50 minutes, when Taro catches up with Jiro, the time will be at 9:06 + 50 minutes = 9:56.
