By adding salt to ice water we lower the freezing point of water (which is the same as the melting point of ice). What that means is the ice which would have normally melted at 32F would now melt at 24F(an approx).
Its important to keep in mind that when 1gm ice melts it absorbs 335 joules (a unit) of heat without raising its temperature(latent heat). In other words, 1 gm of ice would absorb 335joules of heat energy and turn to water while still maintaining the melting point temp.
In case of pure ice water, the ice would absorb that heat energy from the soda at 32F while in the case of ice with salt,it would absorb that energy at 24F.
As the rate of energy transfer is proportional to the square of the temperature gradient. The room temp soda loses heat more quickly to the salt ice water bath(at 24F) than to the pure ice water bath(32F)
Its important to keep in mind that when 1gm ice melts it absorbs 335 joules (a unit) of heat without raising its temperature(latent heat). In other words, 1 gm of ice would absorb 335joules of heat energy and turn to water while still maintaining the melting point temp.
In case of pure ice water, the ice would absorb that heat energy from the soda at 32F while in the case of ice with salt,it would absorb that energy at 24F.
As the rate of energy transfer is proportional to the square of the temperature gradient. The room temp soda loses heat more quickly to the salt ice water bath(at 24F) than to the pure ice water bath(32F)