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# Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 6, November 2019

2019-11-13

## Field Trip to Industry 4.0

How old is the chemical plant and the automation technology it uses?

A group of students goes on a field trip to a chemical plant to experience Industry 4.0 in practice. One student recognizes that the automation technology is modern, but the plant as a whole must be significantly older. The student asks how old the plant and its installed automation technology are. Knowing that the "intelligent" automation technology can answer this question, the chemical plant supervisor challenges the students with the following puzzle:

The chemical plant is seven times as old as the automation technology was, when the chemical plant was as old as the automation technology is today. When the automation technology is as old as the plant is today, the sum of the age of the chemical plant and the automation technology will be 51 years.

How old are the chemical plant and the installed automation technology right now?

## Solution

If you translate the student's question into a mathematical expression, the resulting equations solve for the following two unknown quantities:

c = Age of chemical plant
a = Age of automation technology

The equation referring to the statement “The chemical plant is seven times as old as the automation technology was when the chemical plant was as old as the automation technology is today” is:

c = 7 * ( a – ( c – a))

c = 7 * ( a – c + a)

c = 7 * (2a – c)

c = 14a – 7c

8c = 14a

c = 14a/8

c = (7/4)a

The equation referring to the statement “When the automation technology will be as old as the plant is today, the sum of the age of the chemical plant and the automation technology will be 51 years” is:

c + (c – a) + a + (c – a) = 51

2c – a + a + c – a = 51

3c – a = 51

Plug first equation into second equation:

3 * (7/4)a – a = 51

21/4 a – a = 51

17/4 a = 51 / (: 17/4)

a = 12

According to this, the automation technology is 12 years old today

Plugging this result (a = 12) into the first equation yields the age of the chemical plant.

c = (7/4)a

c = (7/4) * 12 = 21

According to this, the chemical plant is currently 21 years old.

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