Why does salt make boiling water take longer to boil?

Actually, this is a common misconception. Salt does raise the boiling point of water, a phenomenon called boiling point elevation, but the effect is so small in cooking quantities that it makes no practical difference. Adding a tablespoon of salt to a pot of water raises the boiling point by only about 0.5 degrees Celsius or less, which is negligible. In practice, salted water may actually seem to boil faster because salt can slightly reduce water's specific heat capacity, meaning it takes marginally less energy to heat up. The real reason people think salted water takes longer is likely just perception or coincidence in timing when they added the salt.