Problems on Trains

The total distance the train needs to cover to completely cross the platform is the sum of the train's length and the platform's length, which is 120 + 230 = 350 meters. Converting the train's speed to meters per second gives 90 * (5/18) = 25 m/s. Dividing the total distance by this speed yields a time of 14 seconds.

Let the train length be L and its speed be v. The two situations give L + 162 = 18v and L + 120 = 15v. Subtracting yields 42 = 3v, so v = 14 m/s and L = 90 m.

Speed = 50 km/hr = 50 * (5/18) m/s = 250/18 m/s = 125/9 m/s. Time = Distance / Speed = 100 / (125/9) = 900 / 125 = 7.2 seconds.

Let v be speed and L be train length. (L+120)/v = 12 and (L+170)/v = 16. L+120 = 12v and L+170 = 16v. Subtracting gives 50 = 4v, so v = 12.5 m/s.

Convert speed to m/s: 45 km/hr = 45 * (5/18) m/s = 12.5 m/s. Length = speed * time = 12.5 * 10 = 125 meters.

Speed = 72 kmph = 72 * 5/18 = 20 m/s. Time = 1 minute = 60 seconds. Distance = Speed * Time = 20 * 60 = 1200 m. Distance = Train length + Tunnel length. 1200 = 700 + Tunnel length. Tunnel length = 500 m.

Let train length be L and speed be v. L = 15v. (L + 100) = 25v. Substituting L: 15v + 100 = 25v, so 10v = 100, v = 10 m/s. L = 15 * 10 = 150 m.

The total distance to cover is the sum of the train length and the platform length, which is 280 + 220 = 500 meters. The speed of 60 kmph is converted to m/s by multiplying by 5/18, resulting in 50/3 m/s. Time = Distance / Speed = 500 / (50/3) = 500 * 3 / 50 = 30 seconds.

Relative speed = 75 + 50 = 125 kmph. Convert to m/s: 125 * (5/18) = 625/18 m/s. Total distance = 100 + 150 = 250 m. Time = Distance / Speed = 250 / (625/18) = 250 * 18 / 625 = 7.2 seconds.

Total distance = 110 + 132 = 242 m. Speed = 36 km/hr = 36 * (5/18) = 10 m/s. Time = Distance / Speed = 242 / 10 = 24.2 seconds.

The relative speed of the trains is 40 + 32 = 72 km/hr. Converting to m/s: 72 * (5/18) = 20 m/s. The total distance to cover is 121 + 99 = 220 m. Time = distance / speed = 220 / 20 = 11 seconds.

The relative speed of the faster train with respect to the man in the slower train is 56 - 29 = 27 km/hr. Converting to m/s: 27 * (5/18) = 7.5 m/s. Length = speed * time = 7.5 * 16 = 120 m.

Speed = 54 km/hr = 54 * (5/18) = 15 m/s. Distance covered = Speed * Time = 15 * 20 = 300 meters. This distance is the sum of the train length and bridge length. Bridge length = 300 - 100 = 200 meters.

To completely cross the bridge, the train must cover its own length plus the bridge length: 300 + 200 = 500 m. At 25 m/s, the time required is 500/25 = 20 seconds.