does previously boiled water boil faster?

Yes

By boiling water, you don't change the chemical composition of it (unless it contained impurities before). H20 is H20 regardless how many times it has been boiled in the past. From the same starting temperature, both pots will heat up at the same rate.

It depends how long ago the pot was boiled and current temperature of the water. Warm water will boil faster than the colder water.

Not if they start out at the same temperature, but if the temperature of the water in one is greater then the other, it will boil faster because lessenergy will be needed over a smaller period of time to reach it's boiling point.

Assuming you're putting the same amount of energy into both pots of water and then they should both boil at the same rate.

EDIT: To to person above. What if the pot had a lid? Where would the evaporated water go? ;)

Pre-boiled water will boil as quick as any other water at the same temperature. Just about all water has boiled at one time or another.

as long as the water temp is the same when heating begins, then no. The only difference between the two is that the previously boiled water would have less impurities.

ahhahahahhah no. they would boil at the exact same rate.

otherwise i would like to find some water that has been boiled 100 times so when i make pasta it will boil super fast:]

no if the water stays hot than obviously it will boil faster but if it is not like that than no

nope they'd boil just the same as long as the water didn't overgo any physical changes during the first boiling such as mineral ratios etc.