My question is about boiling water.
Which boils first, hot water or cold?
The same amount of hot water, heated at the same rate, in an
identical vessel (pot)
or the same amount of cold water, heated at the same rate (as the hot)
in an identical vessel (to the hot water)

In order to boil any liquid, you must raise its temperature to the
liquid's boiling point. To raise an amount of liquid of mass m by
delta_T degrees you need

E = m*c*delta_T

where m is the mass, c is the heat capacity and delta_T is the
temperature increase. Thus, if you have two amounts of water m_cold
and m_hot which are the same and delta_T_hot < delta_T_cold (since the
hot water is closer to boiling), you will need less energy to bring it
to boiling temperature. Therefore, hot water boils first, since you
are delivering energy at the same rate and require less energy for the
hot water.

As an aside, the energy to actually turn the liquid into gas is given
by

E' = m*l

where m is the mass and l is the latent heat (e.g. heat of
vapourization). Thus the total amount of energy to bring to boil and
vapourise the water is

E+E' = m*(l+c*delta_T)

E' is not important in the comparison since m is the same in both
cases.

Cold water does NOT boil faster than hot water...

Here is the link to the answer the reason why:

http://home.att.net/~aramanujan/physics21.html

Really fun reading too by the way.

Hot water boils first, since cold water needs to reach the hot water
temp and that time would be added to the total time at boiling point,
apparently the reverce is true when FREEZING water, I didn't belive it
but hot water freezes first, try it in your freezer