A partner's help matters !!..

Let the rates of doing work of $X$ and $Y$ be $x$ and $y$ work/day respectively, and $W$ be the work of the job to be completed. Then we have:

$x = 3y$

$\dfrac {W}{y} - \dfrac {W}{x} = 60\quad \Rightarrow \dfrac {W}{y} - \dfrac {W}{3y} = 60 \quad \Rightarrow \dfrac {2W}{3y} = 60\quad \Rightarrow \dfrac {W}{y} = 90$

If $X$ and $Y$ work together the number of days to complete the job is:

$\dfrac {W}{x+y} = \dfrac {W}{3y+y} = \dfrac {W}{4y} = \dfrac {90}{4} = \dfrac {45}{2}$

$\Rightarrow a+b = 45+2 = \boxed{47}$