What speedup can be achieved by using a buffer?

Question

RAM

What speedup can be achieved by using a buffer with an access time 4 times
lower than that of the main memory. Assume it applies 95 percent of the time.
The answer I know is 3.48. But how to decide no. Maybe someone has come across something similar.

Answer 1

The arithmetic mean. They pass at school.
Tbuf = Tmem/4
Tavg = Tbuf*95%+Tmem*5% = Tbuf*0.95+Tmem*0.05 = (Tmem/4)*0.95+Tmem*0.05 = Tmem*(0.95/4+0.05)
acceleration = Tmem/ Tavg = Tmem/Tmem*(0.95/4+0.05) = 1/(0.95/4+0.05) = 3.47826087 ~= 3.48