We study the widths of interspecies Feshbach resonances in a mixture of the fermionic quantum gases 6Li and 4°K. We develop a model to calculate the width and position of all available Feshbach resonances for a system. Using the model, we select the optimal resonance to study the 6Li/4°K mixture. Experimentally, we obtain the asymmetric Fano line shape of the interspecies elastic cross section by measuring the distillation rate of 6Li atoms from a potassium-rich 6Li/4°K mixture as a function of magnetic field. This provides us with the first experimental determination of the width of a resonance in this mixture, ¿B=1.5(5) G. Our results offer good perspectives for the observation of universal crossover physics using this mass-imbalanced fermionic mixture.