Adding salt to water actually boosts the boiling point a few degrees, but even with the higher boiling point, salt water boils faster than pure water because salt water has a lower heat capacity than pure water. This means that it does not take as much energy to boost the temperature of salt water as it does to heat up pure water.
A useful example is a container with 100 grams of pure water compared with a container that has 75 grams of water and 25 grams of salt. When salt enters solution, its heat capacity is just about zero, especially when compared to the heat capacity that water has. A solution with 25 percent salt water heats up about 30 percent more quickly than pure water, which means that it boils first.
This only works if one adjusts the volume of the water so that the salt is a part of the test pot. If one puts two quarts of water into two pots and then adds salt to one, the pure water boils faster. It is only in the pot that has less water, with the salt contributing to the combined mass, that the salt water boils more quickly.