To find the total change in the amount of water in the tank after 6 days, we can follow these steps:
- Determine the hourly decrease in gallons.
- Calculate the total decrease over 6 days.
Step 1: Calculate the hourly decrease. The tank decreases by 10 gallons every 3 hours. Therefore, the hourly decrease is:
\[ \text{Hourly decrease} = \frac{10 \text{ gallons}}{3 \text{ hours}} \approx 3.33 \text{ gallons/hour} \]
Step 2: Calculate the total number of hours in 6 days. There are 24 hours in a day, so in 6 days, the total number of hours is:
\[ 6 \text{ days} \times 24 \text{ hours/day} = 144 \text{ hours} \]
Step 3: Calculate the total decrease over 144 hours. Now, we multiply the hourly decrease by the total number of hours:
\[ \text{Total decrease} = \text{Hourly decrease} \times \text{Total hours} = 3.33 \text{ gallons/hour} \times 144 \text{ hours} \]
However, a simpler approach would be to calculate how many 3-hour intervals fit into 144 hours:
\[ \text{Number of 3-hour intervals} = \frac{144 \text{ hours}}{3 \text{ hours/interval}} = 48 \text{ intervals} \]
Since the tank decreases 10 gallons per interval:
\[ \text{Total decrease} = 10 \text{ gallons/interval} \times 48 \text{ intervals} = 480 \text{ gallons} \]
Final answer: The tank decreases a total of \(-480\) gallons after 6 days.
Therefore, the correct response is −480 gallons.
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