Final answer:
If both the President and the Vice President are unable to serve, the Speaker of the House becomes President.
Step-by-step explanation:
If both the President and the Vice President can no longer serve, the next in line to become President is the Speaker of the House. This line of succession is established by the Presidential Succession Act, which sets forth the order in which officials of the United States government are to act as President in the event that neither the President nor Vice President can perform the duties of the office. According to the current law, after the Speaker of the House, the line of succession continues with the President pro tempore of the Senate, followed by Cabinet members, beginning with the Secretary of State.