Using femtosecond resonant luminescence, we have measured the intersubband scattering fare of electrons in wide GaAs quantum wells at very low excitation densities. Even when the spacing between the first two electron subbands is smaller than the LO phonon energy, we observe that intersubband scattering is a subpicosecond process, much faster than previously measured or anticipated. Our experimental results are in perfect agreement with Monte Carlo calculations, which show that carrier-carrier interaction is responsible for the ultrafast transitions.