A physician conducts a study to investigate the time taken to recover from an ailment under a certain treatment. A group of 82 patients with the ailment are given the treatment, and when they are checked 7 days later, it is found that 9 of them have recovered. The remaining 73 patients are checked 14 days after receiving the treatment, and an additional 15 of them are found to have recovered. If the time to recovery is modeled with a Weibull distribution, estimate the median time to recovery.