Problems on Trains

Let distance be D and speed be S. D/S - D/(S+6) = 4 and D/(S-6) - D/S = 6. Solving these equations yields S=30 and D=720.

Train X speed = D/1.5. Train Y speed = D/1. Relative speed = D(1/1.5 + 1) = D(5/3). Distance = D. Time = D / (5D/3) = 3/5 hours = 36 minutes. 3:00 PM + 36 min = 3:36 PM.

Time to cross pole = Length of train / Speed = 240 / v. Time to cross bridge = (Length of train + Length of bridge) / Speed = (240 + 80) / v = 320 / v. Ratio = 240 / 320 = 24 / 32 = 3 / 4.

Let L1 and L2 be lengths. Speed 1 = 64 km/hr = 17.77 m/s, Speed 2 = 96 km/hr = 26.66 m/s. L1 = 17.77 * 5 = 88.88 m. L2 = 26.66 * 6 = 160 m. Relative speed = 160 km/hr = 44.44 m/s. Time = (88.88 + 160) / 44.44 = 5.6 seconds, which is 5 3/5 seconds.

Speed = 60 km/hr = 60 * (5/18) m/s = 50/3 m/s. Length = speed * time = (50/3) * 30 = 500 meters.

Total distance = 225m + 150m = 375m. Speed = 54 km/h = 54 * (5/18) m/s = 15 m/s. Time = 375 / 15 = 25 seconds.

The speed of the train is 140m / 14s = 10 m/s. To pass a 160m platform, the train must cover its own length plus the platform length, which is 140 + 160 = 300m. The time taken is 300m / 10 m/s = 30 seconds.

Speed = Distance / Time. The train covers its own length to pass a stationary point. Speed = 180 m / 15 s = 12 m/sec.

Total distance to cover = Tunnel length + Train length = 3.5 + 0.25 = 3.75 miles. Speed = 75 mph. Time = Distance / Speed = 3.75 / 75 = 0.05 hours. 0.05 * 60 = 3 minutes.

Total distance = 150m + 300m = 450m. Speed = Distance / Time = 450 / 40.5 m/s. Converting to km/hr: (450/40.5) * (18/5) = 40 km/hr.

Total distance = 200 + 200 = 400 m. Time = 20 s. Speed = 400 / 20 = 20 m/s. Convert to km/hr: 20 * (18/5) = 72 km/hr.

Relative speed = 36 + 45 = 81 km/hr = 81 * (5/18) = 22.5 m/sec. Total distance = Relative speed * time = 22.5 * 20 = 450 m. Length of other train = 450 - 200 = 250 m.

Total distance = 225 + 105 = 330 m. Speed = 54 km/hr = 54 * 5/18 = 15 m/s. Time = 330 / 15 = 22 seconds.