Cook the ripe plantain cubes in a pan with the oil until they are golden. Set aside. Place the rice in a medium saucepan. Then add the butter, water and salt. Bring to a boil over medium-high heat. Stir once, cover, reduce the heat to low, and cook for about 10 minutes. Add the ripe plantains and stir well. Cover again and keep cooking for about 10 minutes more. Remove the pan from the stove and let it sit for 5 minutes. Fluff the rice using a fork and serve immediately.