The reason salt makes water boil faster is because when the salt makes it harder for the water molecules to escape from the pot and enter the gas phase, which happens when water boils.
Adding salt to water is going to do two things to water's physical properties: it will raise the boiling point and it will lower the specific heat.
But lowering the water's specific heat — AKA, the amount of energy needed to change an object's temperature — will cause the salt water to heat up faster!
So yes, salt increases the boiling temperature, but not by very much.
If you add 20 grams of salt to five liters of water, instead of boiling at 100° C, it'll boil at 100.04° C.
So a big spoon of salt in a pot of water will increase the boiling point by four hundredths of a degree!
How can you make water boil faster?
If you're in a hurry, turn your tap to the hottest setting, and fill your pot with that hot tap water.
It'll reach boiling a bit faster than cold or lukewarm water.
You can also get the water even hotter by using your electric kettle.
When you add salt to water, sodium chloride dissociates into sodium and chlorine ions.
The water molecules need more energy to produce enough pressure to escape the boundary of the liquid.
The more salt (or any solute) added to water, the more you raise the boiling point.