To find the total change in the amount of water in the tank after 6 days, we can start by calculating the rate at which the water decreases.
The tank decreases by 10 gallons every 3 hours.
First, let's determine how many 3-hour periods there are in 6 days:
6 days = \(6 \times 24\) hours = 144 hours
Next, we find out how many 3-hour periods are in 144 hours:
\[ \frac{144 \text{ hours}}{3 \text{ hours/period}} = 48 \text{ periods} \]
Then, we calculate the total decrease in water over these 48 periods, with each period causing a decrease of 10 gallons:
\[ \text{Total decrease} = 48 \text{ periods} \times 10 \text{ gallons/period} = 480 \text{ gallons} \]
Since the amount of water in the tank is decreasing, the total change in the amount of water in the tank over the 6 days is a decrease of 480 gallons.
Thus, the answer is:
−480 gallons
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