Using Mach, your Mach number in tenths approx = miles/minute: Mach 0.75 = 7.5 NM/min.
Two head-on aircraft at .75 - .80 will be closing at 15-16 NM/min. With an average detection range of 7 NM, you have 30 seconds or so after visual acquisition. With a nominal 20 NM TCAS display range, you have 1:15 - 1:20 after first display.