A dray moves at the speed of 30 m/m to B point 6000 m away from A point.
When a dray moves 900 m, Taro in A point start to pursue the dray with a ball.
If he catches up with the dray, he put the ball in the dray and he will return toward A point immediately.
He receives a ball at A point and start to pursue the dray again.
Taro repeats this motion until the dray arrives at B point.
The speed of Taro is 90 m/m.
Since Taro begins to move, find the time until he finally puts a ball in the dray since he begins to move at first.
When a dray moves 900 m, Taro in A point start to pursue the dray with a ball.
If he catches up with the dray, he put the ball in the dray and he will return toward A point immediately.
He receives a ball at A point and start to pursue the dray again.
Taro repeats this motion until the dray arrives at B point.
The speed of Taro is 90 m/m.
Since Taro begins to move, find the time until he finally puts a ball in the dray since he begins to move at first.
Answer
150 minutes
Solution
The time for Taro to catch up with the dray at the 1st time is 900 / (90 - 30) = 15 minutes.
The time of returning to A point is 15 minute × 2 = 30 minutes after leaving.
At this time, the dray is moving 900 × 2 = 1800 m from A point.
Since the distance to the dray is twice, the time to catch up with it 2nd time is 15 minutes × 2 = 30 minutes.
The time to return to A point is also 30 minutes.
It is considered as the 2nd time in the same way, the time to catch up 3rd time is 30 minute × 2 = 60 minutes.
When he catches up the 3rd time, the dray is 900. + 30 × (30 + 60 + 60) = 5400 m from A point.
From this, it turns out that the 4th time is impossible.
Therefore, the time until he finally puts a ball in the dray since he begins to move at first is 30 + 60 + 60 = 150 minutes.
150 minutes
Solution
The time for Taro to catch up with the dray at the 1st time is 900 / (90 - 30) = 15 minutes.
The time of returning to A point is 15 minute × 2 = 30 minutes after leaving.
At this time, the dray is moving 900 × 2 = 1800 m from A point.
Since the distance to the dray is twice, the time to catch up with it 2nd time is 15 minutes × 2 = 30 minutes.
The time to return to A point is also 30 minutes.
It is considered as the 2nd time in the same way, the time to catch up 3rd time is 30 minute × 2 = 60 minutes.
When he catches up the 3rd time, the dray is 900. + 30 × (30 + 60 + 60) = 5400 m from A point.
From this, it turns out that the 4th time is impossible.
Therefore, the time until he finally puts a ball in the dray since he begins to move at first is 30 + 60 + 60 = 150 minutes.
