How long does it take to run an MS/MS experiment
The MSMS part is the detection of the LC in this case (nb. you don't need to do LC-MSMS, you can do direct infusion quite happily if you don't need to separate anything), so the actual experiment wouldn't need to take much longer than any other LC (as CHM says).

However, calibration + set-up of these things, and extensive cleaning afterwards, can make it a day's job to run just a few samples (even direct infusion). If you don't have much information on the system already, you may also find that you need to do a 'sighting' run, to work out which ions you need to examine more closely (MSMS). And then there is data processing.....

All in all: quick, if you know exactly what you want, and someone is running everything for you. If you want to argue that it is an easy job, you can, but be aware that this is not always gong to be the case.