To find the total change in the amount of water in the tank after 6 days, we can first figure out how much water is lost in one day.
The tank decreases by 10 gallons every 3 hours. There are 24 hours in a day, so we calculate how many 3-hour periods are in one day:
\[ \text{Number of 3-hour periods in one day} = \frac{24 \text{ hours}}{3 \text{ hours}} = 8 \text{ periods} \]
Now, we calculate the total amount of water lost in one day:
\[ \text{Water lost in one day} = 10 \text{ gallons/period} \times 8 \text{ periods} = 80 \text{ gallons} \]
Next, we determine the total loss over 6 days:
\[ \text{Total water lost in 6 days} = 80 \text{ gallons/day} \times 6 \text{ days} = 480 \text{ gallons} \]
Since the amount of water is decreasing, we express this change as a negative value:
\[ \text{Total change} = -480 \text{ gallons} \]
Thus, the answer is:
−480 gallons
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