The type of word or phrase relationship being used in the sentence "The roads of New Orleans remained flooded due to the hurricane" is cause/effect relationship. This is because the phrase "due to the hurricane" explains the cause (the hurricane) that resulted in the effect or outcome (the roads of New Orleans remaining flooded). To determine the type of relationship being used in a sentence, you need to analyze the context and logic behind the words or phrases and understand how they relate to each other.