Adding a starchy substance such as rice or noodles to boiling water increases the surface tension of the water. When it's just plain water boiling the surface tension of the water can't hold back the force of the steam rising and the bubbles burst. Starches increase this surface tension making the bubbles more elastic/pliable (essentially creating a foam), thus requiring more force for them to burst. This makes the bubbles last longer which allows them to build up and eventually boil over.
It's more likely to occur with anything starchy like rice and pasta.
A lower temperature should help to control a boil over as it will allow the water to cool somewhat and slow the boil.
I'd assume that, from your quoted text, that if you use less water you're still imparting the same amount of starch making a thicker solution. More water would dilute this and bring it closer to normal water. In my own experience, small amounts of water allow lots of bubbles to form but nothing really boils over, it just splatters a bit. But reducing temperature and tilting the lid to let some air in has helped me in the past.
Yes, water does boiler measurably faster with the lid on.
The reason is simple: in order to boil, water must be heated to the boiling point (okay, that was obvious). However, while heat is being introduced at the bottom of the pot, heat is also being lost at the top of the pot, through three means: evaporative cooling, and air convection of heat away from the surface of the water, and radiation from the surface (this last is probably the least significant).
Its like going outside with your hat off--you need to work harder to stay warm, because you are loosing heat faster. Similarly, the flame has to introduce energy to make up for the cooling at the top of the pot.
With the lid on the pot, convective cooling will be substantially curtailed, as cool air will not be able to circulate directly onto the surface of the water to cool it; radiative cooling will be slightly reduced, because heat will have to radiate or convect to the lid, to then radiate from there.
Additionally, with the lid on the pot, the evaporated water cannot diffuse or convect into the room. It will soon reach vapor pressure equilibrium and begin condensing almost as fast as it evaporates, returning much of the latent heat of evaporation as almost as fast as it is lost (it is not a total recovery, because the pot with lid is not air tight).
So the largest of the cooling effects will be curtailed.
The hat is on the pot, as it were :-)
This article at Mind Your Decisions shows actual home experimental measurements. Boiling 16 ounces of water:
The covered pot boiled quicker at 4 minutes and 15 seconds. The
uncovered pot took an extra 30 seconds to boil at 4 minutes and 45
seconds.
You will have to decide if the time difference matters to you. It certainly will cut your electric or gas bill a small amount.
It is the reduced cooling--essentially--insulation like a hat, that is the true effect of the lid.
Best Answer
The scientists tell us the temperature of plain water when it is boiling is 212 degrees F, or 100 degrees C at standard pressure. So it will be very close to that unless you are on a super-high mountain or someplace else where the air pressure isn't what we are used to at sea level.
"Rolling boil" is an expression I have usually seen applied to very vigorous boiling of things other than plain water (like for example when you are making jam, you are boiling water with fruit and lots of sugar in it). However, plain water at a very vigorous boil will still be the same temperature as gently boiling plain water. The difference would be the intensity of the heat source you are cooking it with. If you add heat to your boiling water at a very fast rate, it will boil very vigorously. Gentler heating will make for gentler boiling, but same temperature once boiling starts.
As far as the time it takes to get to that boiling state, that also would depend on your heat source. A little portable camping stove sometimes takes a very long time to boil your pot of water, but a very hot roaring campfire will get it boiling right away. At home, your big burner would be faster than your small burner. So we can't really say how long it will take to come to any type of boil.