In order for your peaches to ripen properly, do not place them in the refrigerator. Simply put them on your counter at room temperature until they reach your desired ripeness, then and only then can you place them in the refrigerator. Upon being placed in the refrigerator, they should last an additional week or so. For maximum flavor, allow your peaches to reach room temperature before eating (about 30 minutes). Once your peaches are sliced, you can add a few dashes of lemon juice or coat with a citric acid solution to prevent excessive browning.