To find the total change in the amount of water in the tank after 6 days, we first need to determine how much water is lost each day.
- The tank loses 10 gallons every 3 hours.
- There are 24 hours in a day.
Now, to calculate how many 3-hour intervals there are in a day: \[ \text{Number of 3-hour intervals in a day} = \frac{24 \text{ hours}}{3 \text{ hours/interval}} = 8 \text{ intervals} \]
Next, we calculate the total loss of water in one day: \[ \text{Water loss per day} = 10 \text{ gallons} \times 8 \text{ intervals} = 80 \text{ gallons} \]
Now, over 6 days, the total change in the amount of water can be calculated: \[ \text{Total water loss in 6 days} = 80 \text{ gallons/day} \times 6 \text{ days} = 480 \text{ gallons} \]
Since the amount of water in the tank is decreasing, the total change in the amount of water in the tank is: \[ \text{Total change} = -480 \text{ gallons} \]
Thus, the total change in the amount of water in the tank after 6 days is \(-480\) gallons.
The answer is \(-480\) gallons.