Answer
$16.875$ minutes
Work Step by Step
First, solve for the volume of the bathtub.
The volume $V$ of a rectangular prism is given by the formula $V=lwh$ where $l$=length, $w$=width, and $h$=height.
Thus, the total volume of the bathtub, noting that $18$ inches is equal to $1.5$ feet, is:
$\begin{align*}
V&=lwh\\
&=(5\text{ feet})(3\text{ feet})(18\text{ inches})\\
&=(5\text{ feet})(3\text{ feet})(1.5\text{ feet})\\
&=22.5\text{ cubic feet}
\end{align*}$
The bathtub is only three-fourths full so the volume of water in the tub is:
$\begin{align*}
\text{volume of water}&=\frac{3}{4} \cdot 22.5\text{ cubic feet}\\
&=16.875\text{ cubic feet}
\end{align*}$
The bathtub drains at a rate of $1$ cubic foot per minute so to determine the time it will take to completely drain the bathtub, divide the water volume by the rate to obtain:
$\require{cancel}
\begin{align*}
\text{time}&=\dfrac{16.875 \text{ cubic feet}}{1 \frac{\text{cubic foot}}{\text{minute}}}\\
\\&=\dfrac{16.875 \cancel{\text{ cubic feet}}}{1 \frac{\cancel{\text{cubic foot}}}{\text{minute}}}\\\
\\&=\dfrac{16.875}{\frac{1}{\text{minute}}}\\
\\&=16.875 \cdot (\text{minute})\\
\\&=16.785\text{ minutes}
\end{align*}$
