Final answer:
The water level in the empty 20-gallon tank rises uniformly to become half full at 10 gallons after 3 minutes of filling. Assuming the emptying rate is the same as the filling rate, the water level then returns to empty in the subsequent 3 minutes. We assume equal rates of change since the question doesn't specify different rates for filling or emptying.
Step-by-step explanation:
When examining how the water level changes in an empty 20-gallon tank, we can utilize our understanding of rates and how they affect volume over time. If we fill the tank at a constant rate for 3 minutes until it is half full, this indicates that the tank, which holds 20 gallons, would have 10 gallons of water after the first 3 minutes. The use of the term 'constant rate' implies that a specific amount of water is being added to the tank each minute. Without an exact rate provided, we can simply state that after 3 minutes, the water level reached half of the tank’s capacity.
Subsequently, if the water is then emptied at a constant rate for another 3 minutes, we apply the same reasoning in reverse. Assuming the emptying rate is the same as the filling rate, the water level would drop from 10 gallons back to 0 gallons by the end of the second 3-minute interval. If the emptying rate differs, the final water level would depend on that new rate, which is not provided in the question.
In summation, during the first 3 minutes, the water level rises uniformly until it reaches half the tank's capacity, and then falls back down to empty over the next 3 minutes, assuming the rates of filling and emptying are the same.