Taro and Hanako ran around the pond to the opposite direction.
When Taro ran 7-laps and Hanako ran 3-laps, they came across exactly at the starting point.
How many times did they passed each other on the way?
Answer
Nine times
Solution
Since Taro takes seven round and Hanako takes three round in the same time, the ratio of the time of one round running is Taro : Hanako = 3 : 7.
It is set to that Taro takes 3 minutes and Hanako takes 7 minutes for one round respectively.
The time until they meets at a starting point is 3 minute × 7= 21 minutes.
The distance of the one round of the pond is set to 21 which is the least common multiple of 7 and 3.
The time of their passing each other is 21/(7+3) = 2.1 minutes and they pass every 2.1 minutes.
The number of times of passing in 21 minutes is 10 times which comes from 21 minute /2.1 minute.
Since the final passing at the starting point is included in 10 times, the number of passing on the way is 10 - 1 = 9 times.
When Taro ran 7-laps and Hanako ran 3-laps, they came across exactly at the starting point.
How many times did they passed each other on the way?
Answer
Nine times
Solution
Since Taro takes seven round and Hanako takes three round in the same time, the ratio of the time of one round running is Taro : Hanako = 3 : 7.
It is set to that Taro takes 3 minutes and Hanako takes 7 minutes for one round respectively.
The time until they meets at a starting point is 3 minute × 7= 21 minutes.
The distance of the one round of the pond is set to 21 which is the least common multiple of 7 and 3.
The time of their passing each other is 21/(7+3) = 2.1 minutes and they pass every 2.1 minutes.
The number of times of passing in 21 minutes is 10 times which comes from 21 minute /2.1 minute.
Since the final passing at the starting point is included in 10 times, the number of passing on the way is 10 - 1 = 9 times.
