Answer :
To solve this problem, we need to find out how long, to the nearest minute, it will take a rain barrel to fill up to 40% of its total capacity in gallons. Here’s how we can do it step by step:
1. Calculate the Volume of the Rain Barrel (in cubic inches):
- The dimensions of the rain barrel are given as 60 inches by 60 inches by 80 inches.
- To find the volume, multiply the length, width, and height:
[tex]\[
\text{Volume} = 60 \times 60 \times 80 = 288,000 \text{ cubic inches}
\][/tex]
2. Convert the Volume from Cubic Inches to Gallons:
- We know that 1 gallon is equal to 231 cubic inches. To convert the volume in cubic inches to gallons, divide the total volume by 231:
[tex]\[
\text{Volume in gallons} = \frac{288,000}{231} \approx 1246.75 \text{ gallons}
\][/tex]
3. Calculate 40% of the Barrel’s Capacity in Gallons:
- To find 40% of the total capacity in gallons, multiply the volume in gallons by 0.4 (which represents 40%):
[tex]\[
\text{40% of volume in gallons} = 1246.75 \times 0.4 \approx 498.70 \text{ gallons}
\][/tex]
4. Determine the Time to Fill the Barrel to 40%:
- The problem requires us to find out how long it will take to fill the barrel with water up to 40% of its capacity. However, without the specific fill rate (the speed at which water fills the barrel measured in gallons per minute), the exact time cannot be determined.
- If a fill rate (in gallons per minute) were provided, you could calculate the time by dividing the 40% capacity in gallons by the fill rate.
Unfortunately, without the fill rate, we can't calculate the time. If additional information about the fill rate is provided, use that value to determine how long it will take to reach 40% capacity.
1. Calculate the Volume of the Rain Barrel (in cubic inches):
- The dimensions of the rain barrel are given as 60 inches by 60 inches by 80 inches.
- To find the volume, multiply the length, width, and height:
[tex]\[
\text{Volume} = 60 \times 60 \times 80 = 288,000 \text{ cubic inches}
\][/tex]
2. Convert the Volume from Cubic Inches to Gallons:
- We know that 1 gallon is equal to 231 cubic inches. To convert the volume in cubic inches to gallons, divide the total volume by 231:
[tex]\[
\text{Volume in gallons} = \frac{288,000}{231} \approx 1246.75 \text{ gallons}
\][/tex]
3. Calculate 40% of the Barrel’s Capacity in Gallons:
- To find 40% of the total capacity in gallons, multiply the volume in gallons by 0.4 (which represents 40%):
[tex]\[
\text{40% of volume in gallons} = 1246.75 \times 0.4 \approx 498.70 \text{ gallons}
\][/tex]
4. Determine the Time to Fill the Barrel to 40%:
- The problem requires us to find out how long it will take to fill the barrel with water up to 40% of its capacity. However, without the specific fill rate (the speed at which water fills the barrel measured in gallons per minute), the exact time cannot be determined.
- If a fill rate (in gallons per minute) were provided, you could calculate the time by dividing the 40% capacity in gallons by the fill rate.
Unfortunately, without the fill rate, we can't calculate the time. If additional information about the fill rate is provided, use that value to determine how long it will take to reach 40% capacity.
