In the question, it is already mentioned that the water tank holds = 24,000 gallons
In the given question it is also mentioned that the need is to find the time required to use 2/3 of the total water that the tank holds.
So the need is to find the amount of water that equals 2/3 of the total water in the tank.
Then
Quantity of water that needed to be used = [24000 * (2/3)] gallons
= 16000 gallons
In the problem it is also mentioned that the average rate of consumption per day is 650 gallons.
So
650 gallons of water used in = 24 hours
16000 gallons of water will be used in = [(24/650) *16000] hours
= 590.77 hours
So the time required to consume 2/3 of the total water in the tank is 590.77 hours.