Question

Tickets for the new ice hockey game went on sale last Sunday morning at the Barclays Center box office. People arrived at the Barclays Center at a rate of 300 per hour starting at 5am until noon, and a queue formed in front of the box office. There was no balking or reneging. At 9am, the box office opened and began selling tickets through 8 ticket windows, each of which served customers at a steady rate of 60 per hour. The box office closed at midday, at which point all remaining people in line were turned away.

I) How many people did the box office serve on Sunday morning?

Answer 1

The box office served 1440 people on Sunday morning, calculated by analyzing the arrival rate, the opening hours of the box office, and the collective service rate of all ticket windows.

Step-by-step explanation:

To calculate the number of people the box office served on Sunday morning, we need to consider both the arrival rate of the people and the service rate of the box office. People arrived at a rate of 300 per hour from 5am to 12pm. The box office opened at 9am and served customers through 8 windows, with each window serving at a rate of 60 per hour.

People were arriving for 4 hours before the box office opened (from 5am to 9am), so the total number of people in line when the box office opened is 4 hours * 300 people per hour = 1200 people. From 9am to 12pm is another 3 hours, so the additional people arriving in that time is 3 hours * 300 people per hour = 900 people. The total number of people who arrived is 1200 people + 900 people = 2100 people.

The total service rate of all 8 windows combined is 8 windows * 60 people per window per hour = 480 people served per hour. Since the box office served from 9am to 12pm, that is 3 hours of service. The total number of people served is 3 hours * 480 people per hour = 1440 people.

Thus, the box office served 1440 people on Sunday morning.