The Story
If you are about to cook something and are waiting for a pot of water to boil, just add some salt to the water and it will heat up faster.
Facts
Saltwater has a lower specific heat than plain water, so yes, an equal weight of saltwater will heat up faster.
But we are considering adding salt to water, so the weights won't be the same. There will be more substance to heat up, which will increase the time.
Yes, we could first remove an amount of water equal in weight to the salt we are going to add and then it would heat faster. But, it would heat even faster if we removed that water and didn't add any salt; there's less water so it heats faster.
Why
This is likely the result of the media and public taking a qualitative scientific fact, ignoring any quantitative factors, and creating significance that doesn't exist.
Belief in this myth is supported by what happens when salt is added to nearly boiling water: the water suddenly starts boiling. In fact it doesn't; it only appears that way. This is the same process as when one adds salt or sugar to soda pop, yet no one claims that the ice-cold drink has become so hot that it boils. The sharp edges of the salt crystals provide nucleation points, and water that is near its boiling point will produce bubbles at those locations.
Adding cold salt to the hot water actually cools it down, making it take more time, not less time, to heat up.