As you grow older, an injury to your ______ may take longer to ______.

The correct option is heel/heal .

To choose the correct words for the blanks, we need to distinguish between the homophones heel and heal based on their meanings and grammatical roles in the sentence:
1. Heel is a noun that refers to the rounded back part of the human foot, below the ankle.
2. Heal is a verb that means to make or become healthy, sound, or whole again after an injury or illness.

Let's look at the blanks in the sentence:
- In the first blank: "...an injury to your ______" requires a noun representing a body part. Therefore, "heel" is the correct choice.
- In the second blank: "...may take longer to ______" requires a verb indicating the process of recovery. Therefore, "heal" is the correct choice.

Putting it all together, the complete sentence is: "As you grow older, an injury to your heel may take longer to heal."