Exploring maths through problem solving

Problem of the Week

Queue Tracking

The British love to assemble in an orderly line. ‘The Queue Tracker’ (https://www.itv.com/news/2022-09-14/official-queen-lying-in-state-queue-tracker-shows-length-and-end-of-line-live) tracked the queue to view Queen Elizabeth II lying in-state at Westminster Hall. On 15 September, it showed the queue to be 4.9 miles long with an estimated wait time of 9 hours. ABC news stated that in the hall, people file each side of the coffin and stop to pay their respects for 10 seconds.

Based on this assumption, how many people on average, would there be per 10 metres of queue?

Is this number realistic? What would be a better estimate of the average stopping time per person?


The last person was estimated to wait 9 hours before reaching the front of the queue.

There are 60 seconds in a minute and 60 minutes in an hour, so 9 hours is 9 x 60 x 60 = 32400 seconds.


If the queue splits in two around the coffin and each person stops for 10 seconds, the number of people to view the coffin in 9 hours would be:   32400 ÷ 10 x 2 = 6480 people.


These people are in a line 4.9 miles long.

4.9 miles is about 7.88579 km.

7.88579 km = 7885.79 m = 788.579 decametres (i.e. 10 metre lengths)

The number of people per 10 metres

= 6480 ÷ 788.579

= approximately 8 people


However, the queue looked to have more than 8 people per 10 metres.

Let’s see what would happen if we halved the average viewing time to be 5 seconds.

32400 ÷ 5 x 2 = 12960 people

The number of people per 10 metres

= 12960 ÷ 788.579

= approximately 16 people.


The shorter viewing time (5 seconds) is perhaps more realistic, or maybe there were some people who paid their respects together with a partner.


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