It depends on the type of peak.
The average, daily peak lasts from around 10 AM to about 5 PM. This is generally from the day-to-day activities from commercial businesses. This kind of peak is routine, expected, and can generally be covered by inexpensive forms of generation.
Extreme, hot-weather peaks generally max out around 4 - 5 PM, though on such days the total load exceeds normal peak by solar noon. The peak is this late in the day because (1) commercial businesses are still open, (2) workers have begun to arrive home and turn on lights, TVs, the AC unit, etc., and (3) the solar energy received during the day is making a very large contribution to the AC cooling requirement (search for "radiant time series." The idea here is that walls store the Sun's energy, and release it later.)
These extreme peaks happen rarely, and the absolute worst lasts for 1 - 3 hours. This is when your jet-fuel burning peakers would come online - they would sit on standby 365 days out of the year, and maybe generate for five hours total.
For the daily peak, in a more diverse area, the natural gas peakers would come on throughout the small daily peak. Rarely would they be on for more than a few hours / day.
15 hours for an extremely expensive fuel type truly is rare.