We apply Honeycutt’s stochastic Runge-Kutta method to the problem of simulating first-passage times. This method quickly and accurately generates discrete values, X(t1), ..., X(t(n)), of distances travelled, but their relatively wide spacing exacerbates the problem of interpolating the time, T(x), to traverse a fixed distance. We use the properties of the three-parameter model to develop an interpolation which yields the correct expected value of T(x). We extend the results of Pickard et al. to larger variances and longer distances. Tle times to traverse successive sections are correlated, but this correlation decreases rapidly with distance and variability (of velocity). The distribution of T(x) is very nearly log-normal and its variance increases linearly with x and the variance of the instantaneous velocity. This confirms a conjecture by Pickard et al.