Answer:
2 hours, 4 minutes and 51 seconds
32 hours 45 minutes and 3 seconds
Explanation:
Volume of sink
[tex]v=lwh\\\Rightarrow v=45\times 56\times 22\\\Rightarrow v=55440\ cm^3[/tex]
Converting gallon to cm³
[tex]1\ gal=3785.41\ cm^3[/tex]
[tex]\\\Rightarrow 0.12\ gal=0.12\times 3785.41\ cm^3=454.2492\ cm^3[/tex]
[tex]\dot v[/tex] = Volumetric flow rate = 454.2492 cm³/min
Time taken
[tex]t=\frac{v}{\dot v}\\\Rightarrow t=\frac{55440}{454.2492}\\\Rightarrow t=122.04754\ minutes[/tex]
Time it takes to overflow the sink is 122.04754 minutes or 2 hours, 4 minutes and 51 seconds
Volume of apartment
[tex]v=350\times \frac{1}{12}\\\Rightarrow v=\frac{175}{6}\ ft^3[/tex]
Converting gallon to ft³
[tex]1\ gal=\frac{1}{7.48052}\ ft^3[/tex]
[tex]\\\Rightarrow 0.12\ gal=0.12\times \frac{1}{7.48052}\ ft^3=0.01604\ ft^3[/tex]
Time taken
[tex]t=\frac{v}{\dot v}\\\Rightarrow t=\frac{\frac{175}{6}}{0.01604}\\\Rightarrow t=1818.37\ minutes[/tex]
Time taken to flood the room would be 122.04754+1818.37 = 1940.41754 minutes or 32 hours 45 minutes and 3 seconds