Does melting ice in sugar water make the ice melt faster?

Answer 1

No, ice melts slower in sugar water compared with distilled water because the addition of the solute will lower the melting point.  This is similar with salt - the addition of either to water will lower the melting point which means the ice will take longer to melt than in water with no solute added.  You will find that ice also melts more slowly in regular soda than in diet soda for similar reasons.  (Of course this is assuming consistency amongst other variables - such as stirring vs. non-stirring.)