A bottle with a volume of 196 U. S. fluid gallons is filled at the rate of 1.08 g/min. In years, how long does the filling take? (The density of water is 1 g/cm3 and 1 U.S. fluid gallon = 231 in3.)
196(231)/(1.08)
The answer given was 1.31 years, not sure of the steps.
you assumed g/min was gallon/minute
Not so. It is grams/minute
So, keeping track of the units, you want to convert volume to time:
196gal * 231 in^3/gal * (2.54cm/in)^3 * 1g/cm^3 * 1min/g = 741940 min = 1.41 yr
Hmmm. check my math or your supposed answer
To find out how long it takes to fill the bottle, we can use the formula:
Time = Volume / Rate
First, let's convert the volume of the bottle from U.S. fluid gallons to cubic inches. We know that 1 U.S. fluid gallon equals 231 cubic inches, so:
Volume (in cubic inches) = 196 U.S. fluid gallons * 231 cubic inches/gallon
Volume (in cubic inches) = 45176 cubic inches
Next, we divide the volume in cubic inches by the filling rate of 1.08 grams per minute:
Time (in minutes) = Volume (in cubic inches) / Filling rate (in cubic inches per minute)
Time (in minutes) = 45176 cubic inches / 1.08 cubic inches per minute
Time (in minutes) ≈ 41837.04 minutes
Now, we need to convert the time from minutes to years. There are 60 minutes in an hour, 24 hours in a day, and approximately 365.25 days in a year, taking into account leap years:
Time (in years) = Time (in minutes) / (60 minutes/hour * 24 hours/day * 365.25 days/year)
Time (in years) ≈ 41837.04 minutes / (60 * 24 * 365.25)
Time (in years) ≈ 41837.04 / 525960
Time (in years) ≈ 0.0796 years
Therefore, the time it takes to fill the bottle is approximately 0.08 years, which when rounded to two decimal places, gives us 0.08 years or approximately 1.31 years.
To find the time it takes to fill the bottle, we need to divide the volume of the bottle by the rate at which it is being filled.
The volume of the bottle is given as 196 U.S. fluid gallons. However, the rate at which the bottle is being filled is given in grams per minute. So, we need to convert the volume from gallons to grams.
We are given that 1 U.S. fluid gallon is equal to 231 in3. To convert this to cm3 (so that we can use the density of water), we need to multiply by the conversion factor 1 in3 = 16.387 cm3.
So, the volume of the bottle in cm3 is:
196 U.S. fluid gallons × 231 in3/U.S. fluid gallon × 16.387 cm3/in3 = 754664.812 cm3
Now, we can convert this volume to grams using the density of water, which is 1 g/cm3.
754664.812 cm3 × 1 g/cm3 = 754664.812 g
Finally, we divide the volume of the bottle by the rate at which it is being filled to find the time.
754664.812 g ÷ 1.08 g/min ≈ 698992.675 min
To convert this time to years, we divide by the number of minutes in a year (assuming a year has 365 days, each with 24 hours, and each hour having 60 minutes).
698992.675 min ÷ (365 days × 24 hours × 60 min) ≈ 1.31 years
Therefore, it takes approximately 1.31 years to fill the bottle.