Final answer:
After one half-life, which is 8 hours in this case, half of the drug will be eliminated. Therefore, 25 mg of the drug will be eliminated by 2:00 PM when administered at 6:00 AM.
Step-by-step explanation:
The question asks us to determine the time when half of the initial dose of a drug has been eliminated from the body, based on the drug's half-life. If the drug's half-life is 8 hours and the nurse administers 50 mg at 6:00 AM, then 25 mg of the drug, which is half of the initial dose, would be eliminated after one half-life. Since one half-life equals 8 hours, adding 8 hours to the initial administration time of 6:00 AM provides the answer: it will be 2:00 PM when 25 mg has been eliminated from the body.