With this perk, your radiation level will decrease by 1 rad every 20 real-world seconds (this doesn't affect accumulation of new rads in any way). Waiting one in-game hour will remove 6 rads. If you had 999 rads, you would have to wait 167 in-game hours to reduce your rad count to zero. The rate applies to fast travel, sleeping and using the wait function.
Fallout: New Vegas
This perk remains functionally identical to the one in Fallout 3. However, Irradiated Beauty exists as a possible alternative.
This perk does not remove rads fast enough to serve as an effective defense against radioactive environments. However, it is useful in preventing the "death from a thousand paper cuts" rad build up, which combined with a high radiation resistance can reduce incidences of serious radiation poisoning to few and far between. It is especially useful in hardcore mode as it effectively eliminates the slow but steady buildup of rads from most food and water.