algebra precalculus - In how many days $Y$ alone finish the work

$X$ and $Y$ do a piece of work in $30$ days .They work together for $6$ days and then $X$ quits and $Y$ finishes the work in $32$ more days.In how many days would $Y$ be able to finish the work alone?

note:$X+Y=1/30$
then $X+Y=6/30=1/5$ finished work
remaining $1-1/5=4/5$ work only by $Y$ in 32 more days
so $\frac54\cdot32=40$ days
is this correct?.