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TB MC Qu$.03-71$ Every student who wishes to enter...

Every student who wishes to enter the public library at Hotel de Ville $($HdV$),$ in the center of Paris, needs to go through the following steps:

a$.$ Show your ID to one of the two guards at the entrance of the HdV building $-20$ seconds

b$.$ Have your bag go through the metal detector$-30$ seconds

c$.$ Give your iD card to the ground floor desk clerk, who will give you in exchange a magnetic badge $-1$ minute

d$.$ Take the stairs up to the fourth floor of the building, where the library is located $-2$ minutes $($Note: multiple people can be on the stairs at the same time$)$

e$.$ Show your badge to one of the two desk clerks at the library entrance to have your badge number archived$-30$ seconds

f$.$ Enter the library and get assigned to a numbered seat by one of the two librarians $-40$ seconds

When the library opens at $9$ a$.$m$.,$ there is usually a very long queue of people waiting to get in$.$ How long does it take for the $25$ seats in the library to be occupied $($assuming there are at least $25$ people in the queue$)?$