A museum only allows patrons to enter at fifteen minute intervals. An observer notices that every weekday at 2:00 there are $8$ people waiting at the entrance and at 3:00 there are $20$ people waiting. In addition, there are $10$ people waiting at the entrance at all 15-minute intervals that are not on the hour. This pattern continues through 6:00. How many people wait to enter the museum in the interval from 2:00 to 6:00?
A) $280$
B) $232$
C) $291$
D) $248$
E) $208$

Question

Quizplus · Accepted Answer

The pattern is: 8 people at 2:00, 10 people at 2:15, 10 people at 2:30, 10 people at 2:45, 20 people at 3:00, and this repeats every hour. From 2:00 to 6:00, there are 4 hours, so the total is $4 \times (8 + 10 + 10 + 10 + 20) = 4 \times 58 = 232$.

A Museum Only Allows Patrons to Enter at Fifteen Minute 888

A Museum Only Allows Patrons to Enter at Fifteen Minute $8$