Answer
$3 \text{ hours}$
Work Step by Step
Let $x$ be the time it takes to empty the tank.
In terms of $1$ unit/part, the rates are related as
\begin{array}{l}\require{cancel}
\dfrac{1}{1.5}-\dfrac{1}{1}=\dfrac{1}{x}
.\end{array}
Using the $LCD=1.5x,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
1.5x\left(\dfrac{1}{1.5}-\dfrac{1}{1}\right)=\left(\dfrac{1}{x}\right)1.5x
\\\\
x(1)-1.5x(1)=1.5(1)
\\\\
x-1.5x=1.5
\\\\
-0.5x=1.5
\\\\
x=\dfrac{1.5}{-0.5}
\\\\
x=-3
.\end{array}
Hence, it takes $
3 \text{ hours}
$ to empty the tank. Note that the negative sign means that water is being drained.
