Put oven rack in the middle position and preheat the oven to 350 degrees F. If necessary, cut off wing tips with poultry shears or a sharp knife. Prick skin of the duck all over with a sharp fork or paring knife. Rub duck inside and out with kosher salt and pepper. Put duck, breast-side up, on a rack inside a roasting pan. Roast for 1 hour and 15 minutes.
Remove the pan from the oven and drain off the fat. Scatter the potatoes and turnips around the edges of the pan, sprinkle with salt and pepper and return the pan to the oven. Roast for 20 minutes, turn the vegetables to coat with any newly rendered fat and roast another 20 minutes. Raise the temperature to 500 degrees. Roast until the skin is crisp and quite brown, about 15 minutes longer.
Remove from the oven; lift the potatoes and turnips from the pan with a slotted spoon, place them in a serving bowl and keep warm. Tent the duck loosely with foil and allow to rest for 10-20 minutes before carving.