Answer :
Answer:
The new extra processor would take 20 hours to download the movie.
Step-by-step explanation:
This word problem presents two variables: [tex]n[/tex] - Processing capacity, dimensionless; [tex]t[/tex] - Download time, measured in hours. Both variables exhibit a relationship of inverse proportionality, that is:
[tex]t \propto \frac{1}{n}[/tex]
[tex]t = \frac{k}{n}[/tex]
Where [tex]k[/tex] is the proportionality constant.
Now, let suppose that original processor has a capacity of 1 ([tex]n = 1[/tex]), the proportionality constant is: ([tex]t = 5\,h[/tex])
[tex]k = n\cdot t[/tex]
[tex]k = (1)\cdot (5\,h)[/tex]
[tex]k = 5\,h[/tex]
The equation is [tex]t = \frac{5}{n}[/tex] and if time is reduced to 4 hours by adding an extra processor, the processing capacity associated with this operation is: ([tex]t = 4\,h[/tex])
[tex]n = \frac{5}{t}[/tex]
[tex]n = \frac{5\,h}{4\,h}[/tex]
[tex]n = 1.25[/tex]
Then, the extra processor has a capacity of 0.25. The time required for the new extra processor to download the movie is: ([tex]n = 0.25[/tex])
[tex]t = \frac{5\,h}{0.25}[/tex]
[tex]t = 20\,h[/tex]
The new extra processor would take 20 hours to download the movie.