The claim turns up in a lot of kitchens: salt the pasta water because it raises the boiling point, and hotter water cooks the pasta faster.
The first half is true. The second half does not survive the arithmetic.
Doing the sum
Dissolving something in water raises its boiling point by a predictable amount:
ΔT = K × m × i
K is a constant for the solvent, 0.512 °C·kg/mol for water. m is molality, moles of solute per kilogram. i is how many particles each unit breaks into. Table salt splits into a sodium ion and a chloride ion, so 2.
Salt is 58.44 grams per mole. A generously salted pot might be 10 grams per liter:
Salt per literBoiling point rises by10 g0.18 °C20 g0.35 °C35 g0.61 °C
That bottom row is roughly seawater. Pasta water at that concentration is unpleasant to eat.
So the honest version is: heavily salted water boils at about 100.2 °C instead of 100 °C. That is a rise of under two tenths of one percent. Your stovetop's own variation across the base of the pan is larger. So is the change from the weather. A passing low-pressure system moves the boiling point by more than the salt does.
Nothing measurable happens to the cooking time.
Then why salt it
Because of the pasta, not the water.
Pasta absorbs water as it cooks, and it absorbs whatever is dissolved in that water along with it. Salting the pot seasons the pasta all the way through while it cooks. Salt added afterwards sits on the outside, and no amount of it produces the same result. You get salty surfaces wrapped around bland starch.
That is the whole benefit, and it is a real one. It just has nothing to do with temperature.
The bit that is genuinely surprising
Salt water can come to the boil sooner than fresh water, which sounds like it contradicts everything above. It does not. Salt water has a slightly lower heat capacity, so the same energy input raises its temperature a little faster. It reaches a boiling point that is marginally higher, and it can get there marginally quicker.
Both effects are tiny. Both are real. Neither is a reason to salt your water. But the next person who tells you salt makes water boil faster is not simply wrong.