Problem of the Week
Problem B and Solution
When Do We Eat?
Problem
Laura is attending a wedding at which 300 guests are present. The guests begin
to leave the celebration at 9:00 p.m., 20 at a time, and thereafter, groups of 20
guests leave at 20-minute intervals.
The bride and groom depart once two-fifths of the guests have left. Right after
that, a late-night buffet is served to the remaining guests.
At what time is the buffet served?
Solution
The buffet is served once 25 of the guests have left, i.e., after 25 × 300 = 120 guests
have left, in groups of 20. Since 120 = 6 × 20 , this means that six groups of 20
guests must leave before the remaining guests get to eat.
The groups of 20 guests at a time start leaving at 9:00 p.m., and exit every 20
minutes after that, the second group at 9:20, the third at 9:40, the fourth at
10:00, the fifth at 10:20, and the sixth at 10:40.
Thus the buffet will be served at 10:40 p.m.