I was looking for the post earlier on in which someone estimated the Sampson radar's line of sight to the horizon to be 16 miles ( was it ? ) versus 13 for SPY radar on A. Burkes....
And doing a bit of advanced math -- Mach 2 X 16 miles or X 13 miles -- how much time until impact does that leave either man/machine system to react?
The post you are probably looking for was by
Naveleye on page 3 - I'll use his figures for mast height and missile speed for the calculations you requested.
Mach 3 at sea level is 2280 miles-per-hour (0.633 miles-per-second). A distance of 13 miles (Aegis) would be covered in 20 seconds and 16.6 miles (Sampson) would be covered in 26 seconds.
Assuming the 1.7 mile minimum engagement distance is the same for whatever system Aegis uses, this distance would be reached only 18/23 seconds after detection (Aegis/Sampson respectively) so either ship has precious little time to detect, react and respond, but the extra 5 seconds the T45 gets might make all the difference.
If you are dealing with a 'slower' mach-2 sea skimmer the Sampson equiped T45 gets 35 seconds before the missile gets into the CIWS range and the Aegis equiped ship gets 27 seconds.