It merely requires a close reading. First, God orders Noah to start loading his family and the animals (Gen 7:1). He warns that the rain will begin in a week (7:4). Then, one week later, when the family and animals are duly loaded, the rains begin and the fountains of the deep open up (7:11). That the loading was complete is reiterated, and Noah and family are shut in by the Lord (7:16). After that, it rains 40 days and nights (7:17). The water rises and rises (“prevailed”; 7:17-19). After 40 days, or shortly thereafter, water covers all (7:20). Everything has died (7:21). Although the text does not specifically say, it was to rain for 40 days and nights, so presumably when the 40 days are over, the rains do end. Finally, the waters bury the earth for 150 days, total, from the beginning of the rains; by my calculation, that means for another 110 days (Gen 7:24). It is possible that the text means the waters continued to cover the earth for a total of 150 days after the last mountaintop was covered.