What power is required to push a train weighing 110,000 kilograms up an incline of 1 in 100 at 20 kilometers per hour, all frictional resistances being neglected?

Power = force times velocity. The velocity you know - it's 20 KPH, but you need to convert this to meters per second. The force is the component of the train's weight that is acting to oppose the movement - so that's 110,000 Kg times g times sin(1/100). Multiply this opposing force (in newtons) by the velocity (n m/s) to get power (in watts).