I may be wrong here:
Adding salt to the water will lower its freezing temperature. Therefore, the water will be liquid at a lower temperature.
We can agree that water at a temperature of 40 degrees centigrade will melt ice slower than water at a temperature of 50 degrees centigrade.
It probably depends on your setup, but if you had enough ice in the water, and added salt, the water temperature would be able to get colder without freezing.. while the water that is locked up in the ice cubes will have no salinity, and a normal melting point.
Something like that?