An express train covers a distance of 600 km between two cities.
(i) Let the original speed of the train be v km/h. Derive a quadratic equation in v given that, if the speed had been increased by 10 km/h, the journey time would have been reduced by 2 hours.
(ii) Solve the quadratic equation obtained in part (i) and write both possible values of v.
(iii) Determine the original speed of the train, clearly explaining why any root, if rejected, is not suitable for this situation.
(iv) Using the speed obtained in part (iii), calculate the actual journey time taken by the train and verify that it satisfies the condition stated in the question.