A bottle with a volume of 190 U. S. fluid gallons is filled at the rate of 1.8 g/min. (Water has a density of 1000 kg/m3, and 1 U.S. fluid gallon = 231 in.3.) In years, how long does the filling take?

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To find the time it takes to fill the bottle in years, we need to follow these steps:

Step 1: Convert the volume of the bottle from U.S. fluid gallons to cubic meters.
1 U.S. fluid gallon is equal to 231 cubic inches. To convert this to cubic meters, we need to multiply by the conversion factors:
1 U.S. fluid gallon = 231 cubic inches * (1 meter / 39.37 inches)^3 = 0.00378541 cubic meters.

So, the volume of the bottle in cubic meters is:
190 U.S. fluid gallons * 0.00378541 cubic meters/ U.S. fluid gallon = 0.7190289 cubic meters.

Step 2: Convert the flow rate of 1.8 g/min to cubic meters per year.
The density of water is 1000 kg/m3. To convert grams to cubic meters, we divide by the density:
1.8 g/min * (1 kg / 1000 g) * (1 min / 60 s) * (1 hour / 60 min) * (1 day / 24 hours) * (1 year / 365 days) = 0.0019063 cubic meters per year.

Step 3: Divide the volume of the bottle by the flow rate to find the filling time in years.
0.7190289 cubic meters / 0.0019063 cubic meters per year = 376.96 years.

Therefore, it will take approximately 376.96 years to fill the bottle.