A 200 meters long train passes a 400 meters long platform in 8seconds. If a girl is walking at a speed of 2 m/sec along the track and thetrain is 3 km and 850 meters away from her, how much time will it take toreach the girl?
Question
A 200 meters long train passes a 400 meters long platform in 8seconds. If a girl is walking at a speed of 2 m/sec along the track and thetrain is 3 km and 850 meters away from her, how much time will it take toreach the girl?
Solution
To solve this problem, we need to break it down into several steps:
Step 1: Determine the speed of the train. The total distance covered by the train to completely pass the platform is the length of the train plus the length of the platform, which is 200m + 400m = 600m. The train covers this distance in 8 seconds. Therefore, the speed of the train is 600m / 8s = 75 m/s.
Step 2: Determine the relative speed of the train and the girl. The girl is moving in the same direction as the train, so we subtract her speed from the train's speed to get the relative speed. This is 75 m/s - 2 m/s = 73 m/s.
Step 3: Determine the distance between the train and the girl. The train is 3 km and 850 meters away from the girl. We need to convert this distance to meters to match the units of our speed. 3 km = 3000 m, so the total distance is 3000m + 850m = 3850m.
Step 4: Determine the time it will take for the train to reach the girl. The time it takes for the train to reach the girl is the distance between them divided by their relative speed. This is 3850m / 73 m/s = approximately 52.74 seconds.
So, it will take approximately 53 seconds for the train to reach the girl.
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