Answer to Question #239399 in Physics for zezo

Question

A bottle with a volume of 198 U. S. fluid gallons is filled at the rate of 1.7 g/min. (Water has a density of 1000 kg/m³, and 1 U.S. fluid gallon = 231 in.³.) How long does the filling take?

Answer 1

Let the volume of the bottle be $V$ and the rate of filling $r=1.7g/min$. The mass of this water is then given as follows:

$$m = \rho V$$

where $\rho=1000kg/m^2 = 1g/cm^3$.

Then the time required to fill the bottle is:

$$t = \dfrac{m}{r} = \dfrac{\rho V}{r}$$

Converting volume to $cm^3$, obtain:

$$V = 198\times 231in^3 = 45738\space in^3 = 749511.53\space cm^3$$

Finally:

$$t = \dfrac{1g/sm^3\cdot 749511.53\space cm^3}{1.7g/min} \approx 440889min\approx 306\space days$$

Answer. $306\space days$.