Should a person pray at the correct time he knows for the prayer, or wait for the Adhan of the area, which is delayed by about an hour and a half, even if he is not praying in congregation?

The five obligatory prayers are not valid if performed before their legally stipulated times. The recognized method for determining prayer times is through the cosmic signs defined by Islamic law. If the questioner can discern the beginning of each prayer's time on her own, she should pray once she has verified it. If she is unable, she should follow a trustworthy muezzin who is knowledgeable of the times. If she can pray in her home with a congregation, this is better and brings greater reward.