The 2017 version of the answer to this question has just been released by the trustees of both pools of money. According to an article in Marketwatch:
“Social Security’s combined trust funds will run dry in 2034, while Medicare’s hospital insurance fund will be exhausted in 2029, the trustees who oversee the benefit programs said Thursday in an annual report.
The latest report, the first during the Trump administration, paints a mildly better picture for Medicare. Last year, trustees said Medicare’s trust fund for hospital insurance would be exhausted in 2028.
Last year, Social Security’s trustees said the program’s two trust funds would be depleted by 2034.
In the report released Thursday, trustees said reserves for the fund that pays disability benefits would be exhausted by 2028. Combined with the fund that pays benefits to retirees, all Social Security reserves would be exhausted by 2034, they said.”