A fifteen year old flat roof that has begun leaking should be reroofed. The money spent on remedial repairs will probably not stop it's accelerated degradation at this age. As for leaving the old roof in place or removing it prior to the installation of the new, first determine the condition of the roof deck (from the underside)making sure that there is no rotting. If the leaks are long term or if they were substantial, you may well have water in the roof system. This also warrants removal. If the roof and deck are dry, reroofing over the old is acceptable, making sure that you are not exceeding the dead load capacity of the structure. Finally, if the carport was built at the same time as the house, reroof it. The economies are there as compared to doing it later.