Thanks to intrinsically short electronic relaxation on the ps time scale, III-V semiconductor unipolar devices are ideal candidates for ultrahigh-speed operation at mid-infrared frequencies. In this work, antenna-coupled, GaAs-based multi quantum-well photodetectors operating in the 10-11`m range are demonstrated, with a responsivity of 0.3A/W and a 3dB-cutoff bandwidth of 100GHz at room-temperature. The frequency response is measured up to 220GHz: beyond 100GHz we find a roll-off dominated by the 2.5 ps-long recombination time of the photo-excited electrons. The potential of the detectors is illustrated by setting up an experiment where the time dependent emission frequency of a quantum cascade laser operated in pulsed mode is measured electronically and in real-time, over a frequency range >60GHz. By exploiting broadband electronics, and thanks to its high signal-to-noise ratio, this technique allows the acquisition, in a single-shot, of frequency-calibrated, mid-infrared molecular spectra spanning up to 100GHz and beyond, which is particularly attractive for fast, active remote sensing applications in fields such as environmental or combustion monitoring.