Problems on Trains

Speed = 36 km/hr = 10 m/s. Length = Speed * Time = 10 m/s * 8 s = 80 m.

Train A speed = 45 kmph = 12.5 m/s. Train B speed = 81 kmph = 22.5 m/s. Relative speed = 35 m/s. In 4s, distance covered = 35 * 4 = 140m. Length A + Length B = 140. Since B = 0.5A, 1.5A = 140, A = 93.33m. Train A passes tunnel in 4 min (240s). Distance = Speed * Time = 12.5 * 240 = 3000m = 3km. Length of tunnel = 3000 - 93.33 = 2.9km, which is approx 3km.

Let L be length, V be speed. L = V * 6. L + 600 = V * 14. Subtracting: 600 = 8V => V = 75 m/s. L = 75 * 6 = 450 m.

Relative speed = 100 - 64 = 36 kmph = 36 * 5/18 = 10 m/s. Distance covered in 40 seconds = 10 * 40 = 400 metres. Since the train overtakes the motorbike, the distance covered is the length of the train.

The relative speed of the train with respect to the man is 40 - 25 = 15 km/h. Converting 15 km/h to m/s gives 15 * (5/18) = 25/6 m/s. The length of the train is speed * time = (25/6) * 48 = 200 meters.

To completely pass through the tunnel, the train must cover a total distance equal to the sum of its own length and the tunnel's length, which is 500 m + 1000 m = 1500 m. Since this distance is covered in 1 minute (60 seconds), the speed is 1500 / 60 = 25 m/s, which converts to 25 * 3.6 = 90 km/hr.

Let train speed be V, Amit speed be A. Train passes Amit: (V-A)*20 = Length. Train passes Sumit: (V+S)*18 = Length. After 10 mins (600s), train meets Sumit. This is a relative speed problem. The time taken to meet is 90 minutes.

Train speed = 222/6 = 37 m/sec. When crossing a man running in the same direction, relative speed = 222/10 = 22.2 m/sec. Man's speed = Train speed - Relative speed = 37 - 22.2 = 14.8 m/sec.

Total distance = 100 + 150 = 250 m. Time = 9 seconds. Relative speed = 250/9 m/s. Convert to km/hr: (250/9) * (18/5) = 100 km/hr. Since they are in opposite directions, relative speed = v1 + v2. 100 = v1 + 40, so v1 = 60 km/hr.

Relative speed = 43 + 51 = 94 km/h = 94 * (5/18) m/s = 26.11 m/s. Length = speed * time = 26.11 * 9 = 235 m.

Relative speed = 25 + 2 = 27 kmph. Convert to m/s: 27 * (5/18) = 7.5 m/s. Time = Distance / Speed = 270 / 7.5 = 36 seconds.

Since the train and the bird are moving in opposite directions, their relative speed is the sum of their speeds: 10 m/s + 5 m/s = 15 m/s. The time taken to cross is the length of the train divided by the relative speed: 120 m / 15 m/s = 8 seconds.

Relative speed = (250+200)m / 45s = 450/45 = 10 m/s. 10 m/s = 36 km/hr. Since they move in the same direction, relative speed = |V1 - V2|. 36 = |27 - V2|. V2 = 27 + 36 = 63 km/hr.