superpus07 wrote:
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 40 times smaller, from source B alone?
A. 6 hours and 40 minutes
B. 15 minutes
C. 12 minutes
D. 10 minutes
E. 3 minutes
Say the time needed to download the movie from source A alone be
a minutes, from source B alone be
b minutes, and from source C alone be
c minutes. Next, since to download the movie from all three sources 2.5 hours (150 minutes) are needed then we have that:
\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{150} (we can sum the rates to get the combined rate of 3 sources).
Also, since to download the movie from A and C alone 4 hours (240 minutes) are needed then we have that:
\frac{1}{a}+\frac{1}{c}=\frac{1}{240}.
Subtract the second equation from the first one:
\frac{1}{b}=\frac{1}{150}-\frac{1}{240} -->
\frac{1}{b}=\frac{1}{400} -->
b=400.
So, to download the movie from source B alone 400 minutes are needed, therefore to download the trailer, which is 40 time smaller than the movies 400/40=10 minutes are needed.
Answer: D.
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66% (04:27) correct
