Hours worked increases with wage So I have been given a utility function = $ 48 R + Ry -R^2$ where $R$ represents leisure hours and $y$ represents labour income. $y=rl$, $r$ is wage rate and $l$ is labour hours. Find hours worked increases with wage.
So what I thought I can do was:

I equate MRS = Slope of Budget constraint and I got something like this 
$(48 + y - 2R)/ R = r $
Then I equated in $R$ and got $R=48+(rl)/r+2$
Can I just now do differential of $R$ with respect to $r$

Can I continue with this method? Have I made some mistake so far? Or is this method completely wrong and is there some other method.
It's probably easiest to insert everything into Utility $U = U(R)$, such that it depends only on one choice variable:

$U(R) = 48R + Rr(L^{*}-R)-R^2$

Deriving w.r.t. $R$ yields the first order condition:

$48 - Rr + r(L^{*}-R)-2R \overset{!}{=} 0$

Rearranging yields leisure in terms of the wage rate:
$R(r) = \frac{48-L^{*}r}{3+r}$

Labor Supply $l(r)$ is hence given by:
$l(r) = \frac{3L^{*}+2rL^{*}-48}{3+r}$

Deriving this by $r$ should yield what you're looking for:

$\frac{d l}{d r} = \frac{3L^{*} + 16}{(r+3)^2}$