Rate Problems: Plugging in Rate Problems - Work as an Invisible Variable
Bill downloads the movie _Revenge of the Avengers_ to his computer
in 2.5 hours using a download manager that downloads from 3 sources
marked $$A$$, $$B$$, and $$C$$. Each source provides download at a constant rate,
but the rates of different sources are not necessarily identical. If
the movie was downloaded from sources $$A$$ and $$C$$ alone, it would take 4
hours to complete the download. The next day, source $$B$$ is available,
but the other sources are inactive. How long will it take to download
the trailer of the movie, a file that is $$\frac{1}{40}$$ the size of the movie, from source
$$B$$ alone?
Now it's easy to calculate the download rate from source $$B$$ alone:
>$$\text{Rate } \color{blue}{[B]} = \text{Rate } \color{blue}{[A+B+C]}- \text{Rate } \color{blue}{[A+C]}$$
>>>$$= 160 - 100$$
>>>$$ = 60 \text{ MB per hour}$$
Which brings us to the final step: The trailer is $$\frac{1}{40}$$ the size of the movie. We have the download rate from source $$B$$, so we have all we need.
| | Rate (MB per hour) | Time (hours) | Work (MB) |
|-------|-------|-------|--------|
| $$A+B+C$$ | $$160$$ | $$2.5$$ | $$\color{green}{400}$$ |
| $$ A+C$$ | $$100$$ | $$4$$ | $$\color{green}{400}$$ |
| $$B$$ | $$60$$ | | $$\frac{\color{green}{400}}{40}=10$$ |
Use this to calculate the time by dividing work by rate:
>$$\displaystyle \text{Time} = \frac{10}{60} = \frac{1}{6} \text{ hours} = 10 \text{ minutes}$$
Incorrect.
[[snippet]]
You weren't asked about the time it would take to download the whole movie. Just the trailer.
Incorrect.
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Incorrect.
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Incorrect.
[[snippet]]
Correct.
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After we __Plug In__ 400 MB as the size of the movie file, we can calculate the download rate when sources $$A$$, $$B$$, and $$C$$ are active:
| | Rate (MB per hour) | Time (hours) | Work (MB) |
|-------|-------|-------|--------|
| $$A+B+C$$ | | $$2.5$$ | $$\color{green}{400}$$ |
Now you can calculate the rate by dividing work by time:
>$$\displaystyle \text{Rate} = \frac{400}{2.5} = 160 \text{ MB per hour}$$
Then we have the download time from sources $$A$$ and $$C$$ alone:
| | Rate (MB per hour) | Time (hours) | Work (MB) |
|-------|-------|-------|--------|
| $$A+B+C$$ | $$160$$ | $$2.5$$ | $$\color{green}{400}$$ |
| $$ A+C$$ | | $$4$$ | $$\color{green}{400}$$ |
Now calculate the rate for $$A$$ and $$C$$:
>$$\displaystyle \text{Rate} = \frac{400}{4} = 100 \text{ MB per hour}$$
6 hours and 40 minutes
15 minutes
12 minutes
10 minutes
3 minutes
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