Friday 29 January 2016

Quibans 16: The London Underground

This is a longer and more involved Quibans, using information taken from an article in the Daily Telegraph.  The article was headed "150 fascinating Tube facts".  I have only reproduced a handful of them below.
London Underground: 150 fascinating Tube facts

1. There is only one Tube station which does not have any letters of the word 'mackerel' in it (*)

2. The average speed on the Underground is 20.5 miles per hour including station stops.

19. Over 47 million litres water are pumped from the Tube each day, enough to fill a standard leisure centre swimming pool (25 metres x 10 metres) every quarter of an hour.

31. Tube trains travelled 76.4 million kilometres last year.

34. The total length of the London Underground network is 250 miles.

90. According to TFL, London Underground trains travel a total of 1,735 times around the world (or 90 trips to the moon and back) each year.

149. The average distance travelled by each Tube train annually stands at around 114,500 miles.

Sometimes we can work something out using one of the statements.  Sometimes we need to combine some of the facts.  What can we work out?

(*)  The first one is included because it is one of my favourite Tube facts.  I was told this by Pete Capewell back in 1995.  (The answer is St John's Wood.)

Here are some possible questions:
  1. What is the average depth of a standard swimming pool?
  2. What is the ratio of the distance of the moon from earth to the circumference of the earth?
  3. What is the ratio of the distance of the moon from earth to the diameter of the earth?
  4. How many trains are there on the London Underground?
  5. How far away is the moon?
  6. Roughly how frequently do the trains run?
  7. How many hours does each train work per day?


Answers:
  1. Using fact 19:  47 million litres of water = 47,000 cubic metres of water (because 1000 litres = 1 cubic metre).  Divide by 24 to get the amount of water per hour and then divide by 4 to get the amount of water pumped out every 15 mins.  This gives the amount of water in a swimming pool as 489.6 cubic metres.  The area of the top of the pool is 25x10 = 250 square metres, which gives an average depth of 1.96m.  As the statement has some "about"s in it then it would be appropriate to give the answer as "about 2m".
  2. Using fact 90:  1735 divided by 180 = 9.6, so the ratio is about 10 : 1.  ("the moon and back" means we divide by 180.)
  3. The circumference is pi times as much as the diameter so we need to multiply by pi.  This gives approx 30:1
  4. Fact 31 tells us the total distance travelled by all of the trains is 76.4 million km, and fact 149 says the average distance travelled by each train is 114,500 miles.  We need to convert so they are in the same units but can then just divide.  76.4 million * 5 / 8 gives 47,750,000 miles.  Dividing this by 114,500 gives 417 trains.
  5. Combining facts 31 and 90 gives us 114,500 miles divided by 180.  This is about 265,000 miles.
  6. Using 31 and 34, we get that the network is traversed abou 191,000 times per year (assuming that every part of the network is traversed the same number of times).  This is 523 times per day.  I think the tube runs for about 19 hours per day, which is 19 x 60 = 1140 minutes.  1140 / 523 results in there being a completed coverage of the map every 2.18 minutes.  So the trains are about 2 mins apart on average.
  7. Using facts 2 and 149, we know that each train does 114500 miles per year and therefore 314 miles per day on average.  Time = Distance / Speed, so 314 / 20.5 gives us 15.3 hours of use per day on average.

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