When travelling to the Algarve last February, we flew into Lisbon and hired a car and drove down to Praia Da Luz in the western Algarve. It sounded like a long way, but the E1 motorway was almost deserted and it only took less than three hours. It was well worth paying the (small) toll charges for an easy journey. Although you should be aware that the transponder which you pay the rental company for only makes it easier for you to pay for the tolls. We thought the transponder fee included the toll charges, but you get billed for that after the hire period is over. But you should consider Lisbon as an alternative to Faro for your Algarve flight.