Quibans 70: Commuting by train

As part of an article about commuting an article from the Daily Telegraph includes an information box.

It gives numbers and what they stand for.  Match them up.

700 million	100 million	2.99 million	139,000	4.6pc
Journeys made by season ticket holders out of Waterloo station alone
Average amount of weekday morning trains at peak times that were overcrowded
Number of people commuting more than two hours per day in 2014, an increase of 72pc in 10 years
The number of journeys made by season ticket holders across the UK in 2014-15.
Number of people forced to stand every morning on peak trains into the capital - an increase of 19,000 in a year

Here is the box in full:

Questions:

1) What percentage of journeys that were made in 2014-15 involve Waterloo station?

2) How many season ticket holders are there?

3) How many people commuted for more than two hours per day ten years previously?

4) What percentage of season ticket holders travelled longer than 2 hours?

5) By what percentage did the number of people forced to stand on trains into London rise by?

6) If that percentage increase continues, how long will it be before half a million people are standing?  Is this realistic?

Answers:

1) 100/700 = 14.2857...%  Given that the two numbers are clearly not exact it would be appropriate to give the percentage as 14%.

2) This is difficult!  700 million journeys per day.  If a passenger takes more than one train does that count as more than one journey?  How many days per year will they travel?  48 working weeks x 5 days = 240 work-days per year, which will be at least 480 journeys (there and back) per person.  Some will take more than one train so let's call that 500 journeys per person on average.  700 million / 500 = 1.4 million commuters.

3) 2.99 million is 172% of the 10-years-ago value.  Back then it was 2.99 million / 1.72 = 1.74 million

4) 139000 out of 1.4 million = 9.9%.  Call it 10%

5)  In the previous year 120,000 people stood on their train and it rose by 19,000.  This is a 15.8% rise (16%)

6) We need 120 * 1.16^n > 500.  Then we need to subtract 1 from n.  Use a spreadsheet to see that n=10 is the first time 500 is breached.  So a further 9 years will be required.  This involves major extrapolation, so is unlikely to be accurate.

Source: http://www.telegraph.co.uk/opinion/2017/09/16/bbc-can-stop-frightfully-middle-class/ 

Quibans 69: QR code of trees

From BBC News:

Chinese maze: Village makes giant tech code from trees

At first glance, it could be the courtly maze of an English country manor - albeit with some rather large gaps.

But a tech-savvy eye will instantly see the green design for what it is - a massive QR code.  These high-tech barcodes are hugely popular in China as a way to make cashless payments on a smartphone.

Xilinshui village, in the northern Hebei province, has created one from trees in a bid to raise its profile.  The design was made from 130,000 Chinese junipers, and can be scanned from above using a phone or tablet.

It is not clear how high above the trees you would have to be to scan it - or how you might get there - but visitors who successfully capture the code will be connected to the village's tourism account on WeChat, a Chinese social media site.

The vast design measures 227m (744ft) along each side, and the trees are between 80cm and 2.5m in height, the South China Morning Post reports.  Xilinshui was named "the most beautiful village in Hebei" in 2015, and received a 1.1 million yuan ($168,000; £124,00) development grant from the province.

Some possible questions:

1) What typo is there in the article?

2) You can see this as being made up of square pixels.  What is the side-length of each pixel?

3) How many juniper trees are there in each pixel?

4) What is the conversion factor between metres and feet?

5) Convert the heights of the trees to feet and inches.

6) What are the conversion factors between the currencies?

7) If they spent all of the development grant money on tress how much was each one?

8) How long might it have taken to plant all of the trees?

Some answers:

1) Typo: “($168,000; £124,00) development grant” – it looks as if a zero is missing from the sterling figure.

2) Side-length of each pixel: I count 37 pixels along each edge, but if the empty border is included then it is 39 by 39.  227 metres divided by 37 is 6.1m, whereas 227m divided by 39 is 5.8m.  Let’s say 6m.

3) Number of trees in a pixel: I counted part of it and then scaled up – I got about 650 tree-filled pixels.  This means there are, on average, 200 trees per pixel.

4) What is the conversion factor between metres and feet?  Remember there are 12 inches in a foot.  3.278 feet is 3 feet 3 inches.

5) 80cm is 2 feet 7 inches.  2.5m is 8 feet 2 inches.

6) Convert currencies: $1 = 6.55 yuan.  £1 = $1.35 £1 = 8.87 yuan.

7) Cost of a tree:  8.46 yuan.  About 95 pence.

8) How long to plant them:  If we assume one minute per tree (because they were very small when planted) and an 8 hour day, five days per week, then it would take one person 54 weeks to plant the trees.  Essentially it is a year.  If we have two people working on this then we can divide the time required.  If it takes longer than a minute to plant a tree (which is likely!) then we will need to multiply.

Source: http://www.bbc.co.uk/news/world-asia-china-41277549