Place the ripe banana or tomato in the brown bag. Ripe fruit gives off ethylene gas, which helps tomatoes to mature.
Add, in a single layer, tomatoes to be ripened. The higher the ratio of unripe tomatoes to ripe fruit, the slower the process will be.
Check the tomatoes each day to see how they are ripening. In general, according to Colorado State Extension, at ambient temperatures of 65 to 70 degrees Fahrenheit, it will take about two weeks for tomatoes to ripen. At lower temperatures, it will take longer.
Remove tomatoes when they achieve the state of ripeness you desire.