Lee can frame $$\frac{1\; cupboard }{x\; days}$$
Ron can frame $$\frac{1\; cupboard }{x+4\; days}$$
So together they can frame
$$\\\frac{1\; cupboard }{x\; days}+\frac{1\; cupboard }{x+4\; days}\\\\
=\frac{(x+4)\; cupboard}{ x*(x+4)days}+\frac{x\; cupboard }{x(x+4)\; days}\\\\
=\frac{(2x+4)\; cupboard}{ x*(x+4)days}\\\\\\$$
Now we know that together they can fram one cupboard in 4 days so
$$\\\frac{(2x+4)\; cupboard}{ x*(x+4)days}\times \frac{4\;days}{1}=1 cupboard \qquad $NOTE: The days cancel out$\\\\\\$$
This gives the equation
$$\\\frac{(2x+4)}{ x*(x+4)}\times \frac{4}{1}=1 \\\\
\frac{4(2x+4)}{ x*(x+4)}=1 \\\\
4(2x+4)=x*(x+4) \\\\
8x+16=x^2+4x \\\\
x^2-4x-16=0 \\\\$$
$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{16}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{2}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}\\
{\mathtt{x}} = {\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{2.472\: \!135\: \!954\: \!999\: \!579\: \!4}}\\
{\mathtt{x}} = {\mathtt{6.472\: \!135\: \!954\: \!999\: \!579\: \!4}}\\
\end{array} \right\}$$
The first answer is invalid
So individually Lee can fram a cupboard in 6.47 days and Ron will take 10.47 days
Exactly the same as CPhill got. These are really tricky. 