Question

Write an equation and then solve each word problem: My computer can download a movie in 5 hours. If I install an extra processor it can download the movie in 4 hours. How long, working alone, would it have taken the new extra processor to download the movie? Pls help me within 10 minutes

Answer 1

Answer:

The new extra processor would take 20 hours to download the movie.

Step-by-step explanation:

This word problem presents two variables: $n$ - Processing capacity, dimensionless; $t$ - Download time, measured in hours. Both variables exhibit a relationship of inverse proportionality, that is:

$t \propto \frac{1}{n}$

$t = \frac{k}{n}$

Where $k$ is the proportionality constant.

Now, let suppose that original processor has a capacity of 1 ($n = 1$), the proportionality constant is: ($t = 5\,h$)

$k = n\cdot t$

$k = (1)\cdot (5\,h)$

$k = 5\,h$

The equation is $t = \frac{5}{n}$ and if time is reduced to 4 hours by adding an extra processor, the processing capacity associated with this operation is: ($t = 4\,h$)

$n = \frac{5}{t}$

$n = \frac{5\,h}{4\,h}$

$n = 1.25$

Then, the extra processor has a capacity of 0.25. The time required for the new extra processor to download the movie is: ($n = 0.25$)

$t = \frac{5\,h}{0.25}$

$t = 20\,h$

The new extra processor would take 20 hours to download the movie.