When heating water on a stove, a full pan of water takes longer to reach the boiling point than a pan that is half full. Why?

Answer 1

If you use the equation for heat released/absorbed to support your explanation,
Q = m*c*(T2 - T1)
where m is the mass, c is the specific heat capacity and T is the temperature.
Since the only substance involved is water, c is the same for both systems. We can also say that the initial and final temperature should be the same for both systems.
Clearly, the other system which has full pan of water has higher mass, and therefore Q needed to heat it is larger, and thus higher amount of time is required for this system.

hope it's clear. :)