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

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

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 (1)/(n)`

`t = (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 = (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 = (5)/(t)`

`n = (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 = (5\,h)/(0.25)`

`t = 20\,h`

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