Monty's Magic Mobile

It is 50 km from Monty's home to where he works.
Monty owns a nifty magic mobile for driving to work. He starts off driving 2 km/hour for the first kilometer. Every kilometer after that, his speed increases instantaneously by 3 km/hour.

What speed is Monty traveling just before he reaches work? How long, to the nearest minute, does his trip to work take?

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