Mach 4 = 1.1801856 KM/s
i.e a missile traveling a Mach 4 will travel 300Km's in 254 seconds, that's 4.23 mins.
As a rule of thumb BVR engagements are at half the actual capacity of the BVR range,
Head on engagement, at a missile launched at 4 mach with the target at say traveling at mach 1, the relative velocity will be mach 5,
@60 KM engagment : 40.67 seconds to impact
@80 KM Engagement: 54.22 Seconds to impact.
Now given the extremely small rcs of a A2A missile, picking up on the Pulse doppler radar is difficult thus most modern A/cs rely on IR and Spectral UV MAWS where detection range is as low as 20 miles, and thus the reaction time of pilot when he actually picks up the alarm tone on the Maws is 13.56 Sec's.
Now you tell me it that is enough for the aircraft to out maneuver a Mach 4 15G missile?