This kitchen myth may have started as a way to encourage people to cook with cold water, not hot, which can contain more impurities. It may also have its origins in the fact that cold water generally gains heat more rapidly than water that is already hot, though it will not boil faster.
But under the right circumstances, the reverse phenomenon can occur, and hot water can freeze more quickly than cool water.
Part of the reason appears to be that hotter water loses mass to evaporation, and because it has less mass, less energy is needed to freeze it. That phenomenon was described as far back as 350 B.C. by Aristotle. The phenomenon is now known as the Mpemba effect, named after Erasto B. Mpemba, a student who noticed it in 1963 while using boiled milk to make ice cream and reintroduced the concept to the scientific literature.
A study published in the American Journal of Physics in 2006 described a number of reasons for the phenomenon.
THE BOTTOM LINE
Cold water does not boil faster than hot water, but hot water can freeze more quickly than cool water.