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We explore the widths of interspecies Feshbach resonances in a mixture of the fermionic quantum gases 6Li and 40K. Experimentally, we obtain the asymmetric lineshape of the interspecies elastic cross section by measuring the distillation rate of 6Li atoms from an optically-trapped 6Li-40K mixture as a function of magnetic field. This provides us with the first experimental determination of the width of a resonance in this mixture, Delta B=1.5(5) G, being one of the broadest. We present an extended version of the Asymptotic Bound-state Model (ABM) and show that this model offers a convenient method to estimate the width and position of a large number of Feshbach resonances. Our results offer good perspectives for the observation of universal crossover physics in this mixture.