The Story
Salt water boils at a higher temperature than pure water, so obviously food in boiling salt water will be in a hotter environment and so will cook faster.
Facts
This is another old wives' tale that is technically true, but in practice not. If you used a whole box of salt and cooked the food in 100% salt-saturated water, you might save a few seconds, but it would hardly be worth the cost or effort and the food would likely become inedible.
The actual difference in boiling temperature caused by adding a little salt to the cooking water is so small that you will never notice the difference.
Why
We cook food in slightly salted water because it tastes better that way. Somewhere, sometime, someone reported that scientists have proven that salt water boils at a higher temperature than normal water, and as usual, the media and general public ignored the difference between qualitative and quantitative results and highly exaggerated its significance.