Peel and slice the turnips thinly, Peel and dice the parsnips (cutting the vegetables small and thin will help speed up cooking time).
Add the sliced and diced vegetables to a large saucepan and cover them with cold water. Add salt to the water and bring to a boil over medium heat. Boil the vegetables for about 8 to 10 minutes until quite soft. Vegetables are cooked when you can easily insert the tip of a knife.
Drain the vegetables and place them back into the saucepan. Add the butter and thyme. With a potato masher, mash all ingredients together. Season with salt and pepper, to taste. Serve warm.