no intermediate stops

[sanju09]

A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 450-mile journey? Assume that the train makes no intermediate stops.

[praxis]

Each hour the train 10h, where h is the hour number.
hour 1: 10 hour 4: 100 hour 7: 280
hour 2: 30 hour 5: 150 hour 8: 360
hour 3: 60 hour 6: 210 hour 9: 450

It will take 9 hours. You can't simply use an integral, because the speed does not increase smoothly.