In the previous question you were provided with an extra piece of information: you were told that only liquid water would be present once equilibrium was established. if the final state of a system is not given, it is still possible to determine it from the initial temperatures and masses. the next few parts will illustrate this point. suppose that in an insulated container, 0.100 kg of water at 20.0∘c is mixed with 1.500kg of ice at −15.0∘c. you are asked to find the final temperature tf of the system, but you are not told what the final phase of the system in equilibrium is.

   
 Latent heat fusion of water, hf = 334 kJ/kg 
 specific heat of water is 4.186 kJ·kgâ’1·Kâ’1 
 specific heat of ice is 2.05 kJ/kgK 
  
 First, lets assume the ice will melt and become liquid water 
 Q in = Q out 
 m1*C(ice)*(0 deg C- (-) 15) + m1*hf + m1*C(water) (Tf - 0))= m2*C(water)*
(T2 - Tf) 
 1.5* 2.05*15 + 1.5*334 + 1.5*4.186*Tf = 0.1*4.186 (20 - Tf) 
 46.125 + 501 + 6.279 Tf = 0.4186 (20 - Tf)... (1)   
 For water if it decrease to 0 deg C, the energy as heat release is 0.4186 (20
- 0) = 8.372 kJ < 46.125 kJ, Lower than Ice which increase temperature from
-10 to zero. So Water will become ice.   
 The energy dissipate for 20 deg C water and change its phase to 0 deg C ice
is still lower than energy absorb by ice to 0 deg C, rearrange the equation.   
 Q in = Q out 
 m1*C(ice)*(Tf- (-) 15) = m2*C(water)*(T2 - 0) + m2*hf + m2*c(ice) (0-Tf) 
 1.5* 2.05* (Tf +15) = 0.4186*20 + 0.1*334 + 0.1*2.05 (-Tf) 
 3.075 (Tf + 15) = 8.372 + 33.4 + 0.205 (-Tf) 
 3.075Tf + 46.125 = 41.772 - 0.205 Tf 
 3.28 Tf = - 4.353 
 Tf = - 1.327 deg C ( Ice phase)

The answer to your question really depends on three things: how much water you have, how cold it is to start out, and how cold the things around it are. water actually freezes when it gets to 32 degrees fahrenheit (0 degrees celsius), but the time it takes to get there may be different.  let's start with the first. if you take two glasses, and fill one with a tiny bit of water, and the other about halfway, then put them both in the freezer, the one with less water will freeze first (you can try this at home, but i recommend using plastic cups and not glass ones).  now let's move on to the second part. let's say you have two glasses, and you fill one with really cold water that has been in the refrigerator, and the other with really hot water from the sink. if you put both of them in the freezer, the one that started out colder will freeze first.  for the third part, let's imagine that you have two glasses with the same amount of water in them, and the water is at the same temperature. imagine putting one outside on a really really cold day in georgia, and having a friend in alaska put one outside on the same day. since it would be so much colder in alaska, the glass of water there would freeze before yours.  so, if you took a tiny bit of really cold water in a glass, and put it outside on a cold day in alaska, it would freeze a lot faster than a big glass of hot water outside on a cold day in georgia.