  We provide exact results for the mean and variance of first-passage times
(FPTs) of making a directed revolution in the presence of a bias in
heterogeneous quenched environments where the disorder is expressed by random
traps on a ring with period $L$. FPT statistics are crucially affected by the
disorder realization. In the large-$L$ limit, we obtain exact formulae for the
FPT statistics, which are described by the sample mean and variance for waiting
times of periodically arranged traps. Furthermore, we find that these formulae
are still useful for nonperiodic heterogeneous environments; i.e, the results
are valid for almost all disorder realizations. Our findings are fundamentally
important for the application of FPT to estimate diffusivity of a heterogeneous
environment under a bias.
