Problems on Trains

Speed of the train in m/s = (72 * 1000) / 3600 = 20 m/s. Length of the train = Speed * Time = 20 * 10 = 200 meters.

Speed = Distance / Time. Distance covered by the train in passing the telegraph pole = Length of the train. Distance covered by the train in passing the platform = Length of the train + Length of the platform. Therefore, Speed of the train = (Length of the train + 250 meters) / 25 seconds. Since the length of the train is not given, we cannot calculate the exact speed of the train. However, we can say that the speed of the train is greater than 45 km/h (which is the speed required to cover 250 meters in 25 seconds) and less than 72 km/h (which is the speed required to cover 250 meters + the length of the train in 25 seconds).

First, we need to convert the speed of the train from kilometers per hour to meters per second. (72) kilometers per hour is equal to (72 \times 1000 / 60 / 60 = 20) meters per second. Then, we can use the formula (distance = speed \times time) to find the length of the train. The distance traveled by the train in (30) seconds is (20 \times 30 = 600) meters. Therefore, the length of the train is (600) meters.

To find the length of the train, we need to convert the speed of the train from kilometers per hour to meters per minute. 60 kilometers per hour is equal to 60 * 1000 / 60 = 1000 meters per minute. Since the train crosses a 1-kilometer-long bridge in 1 minute, the length of the train must be 1000 - 1000 = 200 meters.

Let (x) be the speed of the train on the return trip. Then, the time taken for the trip from City A to City B is (300/60 = 5) hours and the time taken for the return trip from City B to City A is (300/x) hours. Since the return trip takes 1 hour longer than the trip from City A to City B, we have (300/x = 5 + 1 = 6). Solving for (x), we get (x = 300/6 = 50) miles per hour. Therefore, the speed of the train on the return trip is 50 miles per hour.

Relative speed = 72 + 18 = 90 km/h = 90 * (5/18) = 25 m/s. Time = Distance / Speed = 175 / 25 = 7 seconds.

The speed of the train is 180 m / 20 s = 9 m/s. To cross a 216 m platform, the train must cover its own length plus the platform length, which is 180 + 216 = 396 m. The time taken is 396 m / 9 m/s = 44 seconds.

The relative speed of the train with respect to the man is unknown because the man's speed is not provided. Therefore, the length of the train cannot be determined.

Relative speed = 20 + 30 = 50 km/hr. Time to meet = 500 / 50 = 10 hours. Distance from X = 20 km/hr * 10 hr = 200 km.

To cross the bridge completely, the train must cover its own length plus the bridge length, 100 + 10 = 110 m. The speed is 70 km/h = 19.44 m/s, so the time is 110/19.44, approximately 5.65 seconds.

Relative speed = 60 - 30 = 30 km/hr = 30 * 5/18 m/s = 150/18 = 25/3 m/s. Distance = Speed * Time = (25/3) * 30 = 250 m.

Relative speed = 40 - 10 = 30 km/hr = 30 * (5/18) m/s = 25/3 m/s. Distance to cover = 200 m. Time = 200 / (25/3) = 200 * 3 / 25 = 24 seconds.

Speed = 54 kmph = 54 * (5/18) = 15 m/s. Distance covered in 60 seconds = 15 * 60 = 900 meters. Since the train crosses a 500m platform, the train length = 900 - 500 = 400 meters.

Let the length of each train be L. Speed of train 1 = L/3. Speed of train 2 = L/4. When moving in opposite directions, relative speed = L/3 + L/4 = 7L/12. Time to pass each other = (L + L) / (7L/12) = 2L / (7L/12) = 24/7 seconds.