  We consider the mean first passage time of a random walker moving in a
potential landscape on a finite interval, starting and end points being at
different potentials. From analytical calculations and Monte Carlo simulations
we demonstrate that the mean first passage time for a piecewise linear curve
between these two points is minimised by introduction of a potential barrier.
Due to thermal fluctuations this barrier may be crossed. It turns out that the
corresponding expense for this activation is less severe than the gain from an
increased slope towards the end point. In particular, the resulting mean first
passage time is shorter than for a linear potential drop between the two
points.
