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You can do the math. Fentanyl lozenges-approx. 7 hours. Duragesic takes a few hours to kick in and is supposed to last up to 72 hours (like how Oxycontin is supposed to last 12 hours) but most people find it lasts 36-60 hours. From my experience I've found fentanyl patches to last about 48-54 hours.
Methadone half-life: The half-life of Methadone is 15 to 60 hours. It takes five times the half-life to leave your system. Therefore it could take anywhere between 75 hours to 300 hours to clear your system. This is with chronic use.