Problems on Trains

Speed = 36 km/hr = 10 m/s. Distance = Speed * Time = 10 m/s * 6 s = 60 m.

Let L be the length of the train and v be the speed. L = v * 10. (L + 2000) = v * 110. Substituting L: 10v + 2000 = 110v. 100v = 2000, so v = 20 m/s. 20 m/s * 18/5 = 72 kmph.

The train's speed is 108 km/h = 30 m/s. In 12 seconds it covers 360 m, so the platform is 360 - 280 = 80 m long, and the boy's speed is 80/10 = 8 m/s.

At 90 km/hr, the train travels 25 metres per second. In one minute, it covers 1500 metres, which equals the train length plus the platform length. Since these lengths are equal, the train length is 1500/2 = 750 metres.

Speed = 144 km/h = 144 * (5/18) m/s = 40 m/s. Time = Distance / Speed = 100 / 40 = 2.5 seconds.

Total distance = 700 + 500 = 1200 m. Speed = 54 km/h = 54 * (5/18) = 15 m/s. Time = 1200 / 15 = 80 seconds.

Speed = 66 kmph = 66 * (5/18) m/s = 55/3 m/s. Length of train = Speed * Time = (55/3) * 18 = 55 * 6 = 330 m.

Train speed = 25 km/hr = 25 * (5/18) m/s. Time to pass platform = 18s. Length of train + platform = speed * time = (25 * 5/18) * 18 = 125 m.

The train covers its own length plus the platform length (75 + 75 = 150 meters) in 15 seconds. Speed = distance / time = 150 / 15 = 10 m/s.

Total distance = 110 + 132 = 242m. Speed = 72 km/hr = 72 * (5/18) = 20 m/s. Time = 242 / 20 = 12.1 seconds.

Relative speed = 45 - 40 = 5 km/hr = 5 * (5/18) m/s = 25/18 m/s. Total distance = 200 + 150 = 350 m. Time = Distance / Speed = 350 / (25/18) = 350 * 18 / 25 = 14 * 18 = 252 seconds.

Speed of the train = distance / time = 110 m / 3 s = 110/3 m/s. To cross a 165 m platform, the train must cover its own length plus the platform length: 110 + 165 = 275 m. Time = 275 / (110/3) = 275 * 3 / 110 = 7.5 seconds.

Let train length be L and speed be v. (L + 275) / 15 = v and (L + 425) / 21 = v. Equating: (L + 275) / 15 = (L + 425) / 21. 21L + 5775 = 15L + 6375. 6L = 600, so L = 100.

Relative speed = 49 + 5 = 54 km/hr = 54 * (5/18) = 15 m/s. Length of train = speed * time = 15 * 12 = 180 m.

Relative speed = 46 - 10 = 36 km/hr = 36 * (5/18) = 10 m/s. Time = 22 sec. Length = Speed * Time = 10 * 22 = 220 m.