Will food cook faster in salt water?

The answer is: yes

Salt raises the boiling point of water. In fact, for every 10 grams of salt added to a liter of water, the boiling point increases by about 0.5 degrees Celsius (0.9 degrees Fahrenheit). This means that water with salt will take longer to boil than pure water.

Conversely, however, salting the water will also raise the boiling point of the food being cooked, meaning it will cook faster than in pure water.