  We consider first-passage percolation on a ladder, i.e. the graph
{0,1,...}*{0,1} where nodes at distance 1 are joined by an edge, and the times
are exponentially i.i.d. with mean 1. We find an appropriate Markov chain to
calculate an explicit expression for the time constant whose numerical value is
approximately 0.6827. This time constant is the long-term average inverse speed
of the process. We also calculate the average residual time.
