同志们，看看俺工科博士的解题！

Assumption first:

t0 -- minutes of queueing before opening of gates
X --- number of people coming per minute
Y --- passing rate of people per gate per minute

so,

40 minutes after opening of 3 gates -->

(40+t0)*X = 40*Y*3

25 minutes after opening of 4 gates -->

(25+t0)*X = 25*Y*4

Using the above 2 equations to derive the following -->

(10+t0)*X = 10*Y*8

which means that 10 minutes to clear all the people.

haha!