Your mother uses a pan to cook chicken for your dinner. Explains the reason why she cooks faster when the pan?

When the pan doesn’t make sense, but if you mean, “Why can you cook faster with a pan than without one?,” the answer is that the pan concentrates and retains the heat from the stove, making the chicken cook more quickly and evenly than if the chicken were cooked over a fire without a pan.

When the pan ..is covered? If that is the question, it is because covering thew pan minimizes evaporation(hence loss of latent heat of vapourization, and reduces radiant heat los from the pan.