Train leaves A station every 15 minutes.
Every train stops at A station for 2 minutes.
Taro is moving by bicycle at the speed of 175 m/m to the opposite direction of the train on the road along the railroad.
Taro passed by the train which left A station at 8:00 at 4350 m point from the A station. Moreover, Taro passed by another train which left A station at 8:15 at 2100 m point from the A station.
Find the distance (m) from A station of the point where Taro who passed A station passes by the train which is scheduled to leave A station at 8:45.
Answer
2100 m
Solution
The time Taro moves 4350 - 2100 = 2250 m by bicycle is 2250 / 175 = 90/7 minutes.
As train leaves A station every 15 minutes, the interval of trains is also 15 minutes.
The distance train moves in 15 - 90/7 = 15/7 minutes is same as the distance Taro(bicycle) moves in 90/7 minutes.
Thus the train's speed is 2250 / 17/7 = 1050 m/m.
As 2100 / 1050 = 2 minutes, the time when Taro passed by next train is 8:15 + 0:02 = 8:17.
Furthermore, as 2100 / 175 = 12 minutes, the time when Taro passed by A station is 8:17 + 0:12 = 8:29.
The train leaves A station at 8:45 will arrive at A station 8:43.
At 8:29 the train is at 1050 × (43 - 29) = 14700 m behind A station.
The distance of the point where Taro passes the train is 14700 × 175/(1050+175) = 2100 m.
Every train stops at A station for 2 minutes.
Taro is moving by bicycle at the speed of 175 m/m to the opposite direction of the train on the road along the railroad.
Taro passed by the train which left A station at 8:00 at 4350 m point from the A station. Moreover, Taro passed by another train which left A station at 8:15 at 2100 m point from the A station.
Find the distance (m) from A station of the point where Taro who passed A station passes by the train which is scheduled to leave A station at 8:45.
Answer
2100 m
Solution
The time Taro moves 4350 - 2100 = 2250 m by bicycle is 2250 / 175 = 90/7 minutes.
As train leaves A station every 15 minutes, the interval of trains is also 15 minutes.
The distance train moves in 15 - 90/7 = 15/7 minutes is same as the distance Taro(bicycle) moves in 90/7 minutes.
Thus the train's speed is 2250 / 17/7 = 1050 m/m.
As 2100 / 1050 = 2 minutes, the time when Taro passed by next train is 8:15 + 0:02 = 8:17.
Furthermore, as 2100 / 175 = 12 minutes, the time when Taro passed by A station is 8:17 + 0:12 = 8:29.
The train leaves A station at 8:45 will arrive at A station 8:43.
At 8:29 the train is at 1050 × (43 - 29) = 14700 m behind A station.
The distance of the point where Taro passes the train is 14700 × 175/(1050+175) = 2100 m.
