Ron takes approximately $\boxed{4.2}$ hours to make $100$ crusts alone.
Since we are given that:
Number of hours taken by Ron before Harold = 1.2 hours
Number of hours taken by Ron and Harold together = 1.8 hours
We need to find the number of hours taken by Ron alone i.e. $'x'$.
Let the number of hours taken by Harold alone be $'1.2-x'$.
Let the work done by Ron alone=$1/x$
Let the work done by Harold alone=$1/(x-1.2)$
We get that:
$\frac{1}{x}+\frac{1}{x-1.2}=\frac{1}{1.8}$
$\frac{x-1.2+x}{x(x-1.2)}=\frac{1}{1.8}$
$\frac{2x-1.2}{x^2-1.2x}=\frac{1}{1.8}$
$3.6x-2.16=x^2-1.2x$
$x^2-1.2x-3.6x+2.16=0$
$x^2-4.8x+2.16=0$
$(x-0.5)(x-4.2)=0$
$x$ can be either $0.5$ or $4.2$ to satisfy the equation
$x-1.2$ is negative with $x = 0.5$, so $x = 4.2$ is the only solution
Hence, Ron takes approximately $\boxed{4.2}$hours to make 100 crusts alone.
