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Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 2, July 2017

2017-06-08

Field trip to Industry 4.0

Industry 4.0 at a chemical plant
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 in order 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 could 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

Translating the student's challenge question into a mathematical expression, these equations solve for the following two unknown quantities:

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

The equation referring to the first 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 second 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


Insert 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, today, the automation technology is 12 years old.

 

Inserting 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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