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The mean absorption time $T(x,v)$, where $x$ and $v$ denote the initial position and velocity, was calculated exactly by Masoliver and Porr\\`a in 1995. We consider a more general boundary condition. On arriving at either boundary, the particle is absorbed with probability $1-p$ and reflected with probability $p$. The reflections are inelastic, with coefficient of restitution $r$. 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