  Mass-loss rate, $\dot{M}$, is one of the key parameters affecting evolution
and observational manifestations of massive stars, and their impact on the
ambient medium. Despite its importance, there is a factor of ~100 discrepancy
between empirical and theoretical $\dot{M}$ of late-type O dwarfs, the
so-called weak-wind problem. In this Letter, we propose a simple novel method
to constrain $\dot{M}$ of runaway massive stars through observation of their
bow shocks and Stromgren spheres, which might be of decisive importance for
resolving the weak-wind problem. Using this method, we found that $\dot{M}$ of
the well-known runaway O9.5 V star zeta Oph is more than an order of magnitude
higher than that derived from ultraviolet (UV) line-fitting (Marcolino et al.
2009) and is by a factor of 6 to 7 lower than those based on the theoretical
recipe by Vink et al. (2000) and the Halpha line (Mokiem et al. 2005). The
discrepancy between $\dot{M}$ derived by our method and that based on UV lines
would be even more severe if the stellar wind is clumpy. At the same time, our
estimate of $\dot{M}$ agrees with that predicted by the moving reversing layer
theory by Lucy (2010).
