The Chain Rule & Implicit Differentiation · Hard problem

A particle moves along the curve $xe^y + ye^x = 1$, which has no simple explicit formula for $y$ in terms of $x$. At the instant it passes through $(0,1)$, its $x$-coordinate is increasing at $2$ units per second and its $y$-coordinate is decreasing. At this instantaneous rate, how many seconds would it take for $y$ to decrease by $1$ unit?