  Understanding the role of mergers in galaxy formation is one of the most
outstanding problems in extragalactic astronomy. While we now have an idea for
how the merger fraction evolves at redshifts z < 3, converting this merger
fraction into merger rates, and therefore how many mergers an average galaxy
undergoes during its history, is still uncertain. The main reason for this is
that the inferred number of mergers depends highly upon the time-scale
observational methods are sensitive for finding ongoing or past mergers. While
there are several theoretical and model-based estimates of merger times, there
is currently no empirical measure of this time-scale. We present the first
observationally based measurement of merger times utilising the observed
decline in the galaxy major merger fraction at z < 1.2 based on > 20,000
galaxies in the Extended Groth Strip and COSMOS surveys. Using a new
methodology described in this paper, we determine how long a galaxy remains
identifiable as a merging system within the CAS system. We find a maximum CAS
major merger time-scale of 1.1+/-0.3 Gyr at z < 1.2, and a most likely CAS
merger time-scale of 0.6+/-0.3 Gyr, in good agreement with results from N-body
simulations. Utilizing this time-scale we measure the number of major mergers
galaxies with masses M_{*} > 10^{10} M_0 undergo at z < 1.2, with a total
number N_m = 0.90_{-0.23}^{+0.44}. We further show that this time-scale is
inconsistent with a star formation origin for ultra-high asymmetries, thereby
providing further evidence that structural methods are able to locate mostly
merging galaxies.
