This was quite a challenging question. Contrary to what another scientist suggested, the difference in heat capacity between fresh and saltwater is actually very small. In other words, freshwater and saltwater heat up or cool down about as slowly as one another, and therefore have about the same ability to heat or cool other things they are in contact with.

At first glance at the question, I thought that the question was incorrectly worded, because I originally suspected that saltwater would melt ice cubes faster than freshwater (which is the opposite of what you found). This is because adding salt to water lowers its freezing point, requiring that the water be cooled to a lower temperature in order to form ice. This is why they salt roads -- it melts the ice on the roads by lowering its freezing point and it prevents water on the roads from freezing and forming ice. However, your question was stated correctly.

An ice cube indeed will melt faster in freshwater than in saltwater, despite the fact that salt lowers the freezing temperature of water and prevents the formation of ice (this effect is called "freezing point depression"; interestingly enough, adding salt to water will also increase its boiling point as well, called "boiling point elevation", thereby increasing the range of temperature at which water remains in the liquid form).

The reason an ice cube melts faster in freshwater than saltwater is due to an entirely different process than the one that causes salt to prevent ice formation at low temperatures. When I realized that you question was an accurate one, I then mistakenly thought that maybe ice melts slower in saltwater because saltwater is more dense than freshwater. Have you ever noticed that you can float higher/better in the ocean than in a lake? This is because the amount of water that you displace is equal to your body weight. Therefore, since saltwater is denser, you displace less of it and float higher.

For an ice cube, the fact that saltwater is denser causes more of the ice cube float higher in saltwater than in freshwater. This exposes a greater surface area of the ice cube to the surrounding water in freshwater as compared to in saltwater, where the ice cube floats higher and displaces less water. The more surface area of the ice cube in contact with the water, the faster it will melt, right? Well, it turns out that the difference in density between ocean water and freshwater is only about 3%, so only 3% more of the ice cube will be submerged in freshwater than in saltwater. So then, what is the correct answer?

One way to find out is to do an experiment where you place ice cubes into 2 saltwater glasses and 2 freshwater glasses that are all filled with water at the same temperature (you should actually use 4 or more glasses of each type of water in order to replicate the experiment and see whether your results are consistent). Drop some dye (food coloring) onto the ice cube in each of the glasses, and then start stirring half of the freshwater glasses and half of the saltwater glasses. Leave the other glasses unstirred and watch what happens to the dye and which ice cubes melt fastest or slowest. You should find that the ice cubes melt fastest in the stirred saltwater and freshwater glasses. In both of these stirred glasses, the dye should mix throughout the water. In contrast, for the unstirred glasses, the ice melts faster in freshwater than in saltwater. However, the dye stays at the top of the unstirred saltwater glass whereas the dye mixes throughout the unstirred freshwater glass.

It then appears that the reason the ice cube melts slower in unstirred saltwater than in unstirred freshwater or in stirred water (either salt or fresh) is somehow linked to the observation that the dye stays at the top of the unstirred saltwater glass and does not mix or spread through the water in unstirred saltwater.

The dye mixes through the STIRRED glasses because the stirring causes turbulence that tends to homogenize the glass of water, causing the dye to diffuse throughout the glass. The result is that the cold water around the melting ice is mixed and is replaced by warmer water from other parts of the glass. This mixing helps to break up a cold "boundary layer" of melted ice water that forms around and insulates the ice cube, and therefore exposes the ice to warmer water and melts it faster.

When the dye mixes throughout the UNSTIRRED FRESHWATER glass, this indicates a slightly different process called "convective cooling." In convection, a cold fluid is denser than a warm fluid, so the warm fluid tends to rise above the cold fluid and pushes the cold fluid below it. In the freshwater glasses,the ice cube cools the top layer of water as it melts, forming fresh ice water. This cold ice water is denser than the rest of the glass of freshwater, and tends to sink to the bottom of the glass.

I am not sure. Offhand I would expect the opposite to happen. I assume that the salt water and tap water were the same temperature. If so, I would guess that the reason would be as follows:

Water has a huge heat capacity, meaning that the amount of energy required to raise a given volume of water by a certain number of degrees is much greater than the amount of energy required to do the same to most every other substance around.

Saltwater is not pure water, and the salts in it change (lower) the heat capacity of the fluid. As a result, the ice cube cooled off the saltwater immediately around it that it did not with the tap water, and thus the temperature difference between the ice cubes and saltwater was smaller than that with the tap water, and thus the ice cube picked up energy less rapidly by Newton's Law of Cooling.