Recently, Chartas et al. detected a rapid X-ray. are in the gravitationally lensed, multiple-image quasar RX J0911.4+ 0551. Dramatic events, such as rapid X-ray flares, are useful for providing high-precision measurements of the time delays between multiple images. In this paper we argue that there is a new possibility for measuring time delays between multiple images of gravitationally lensed quasars and constraining the locations of putative flares that give rise to the intrinsic rapid variabilities of quasars. The realization of these goals, however, cannot be achieved at present because of the limited accuracy of the current measurements. We predict that timing flares with accuracies of the order of a few seconds will be needed to probe the location of the flares. The method that we are proposing will work with better instruments in near future, such as the X-Ray Evolving Universe Spectroscopy Mission.