SOLUTION: At 5:12:40 PM Bob starts downloading a 952MB media file at 16.5Mbps.
At 5:15:02 PM Alice starts downloading the same media file at 30.2 Mbps.
a) How many seconds will it take
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-> SOLUTION: At 5:12:40 PM Bob starts downloading a 952MB media file at 16.5Mbps.
At 5:15:02 PM Alice starts downloading the same media file at 30.2 Mbps.
a) How many seconds will it take
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Question 1177907: At 5:12:40 PM Bob starts downloading a 952MB media file at 16.5Mbps.
At 5:15:02 PM Alice starts downloading the same media file at 30.2 Mbps.
a) How many seconds will it take for Bob and Alice to download the file?
b) Plot the graph of downloaded filesize vs. time for both Bob and Alice.
c) How many seconds will it take for Alice have exactly the same partially downloaded filesize as Bob?
x = 0 seconds at 15:12:40 pm.
x = 142 seconds at 15:15:02 pm.
bob downloads at 16.5 megabits per second.
alice downloads at 30.2 megabits per second.
the file size is 952 megabytes.
one byte is equal to 8 bits.
downloading at 16.5 megabits per second / 8 = 2.0625 megabytes per second.
downloading at 30.2 megabits per second / 8 = 3.775 megabytes per second.
the straight line equation for bob is y = -2.0625 * x + 952
the straight line equation for alice is y = 3.775 * (x - 142) + 952.
the equation for alice uses (x - 142) rather than x because alice starts 142 seconds after bob.
the calculations for determining that alice starts 142 seconds after bob are:
5:15:02 minus 5:12:40 = 5:14:62 minus 5:12:40 = 0:2:22 = 0:0:142.
0:0:142 is equal to 142 seconds.
for bob, 952 MB / 2.0625 = 461.2757576 seconds to download the file.
for alice, 952 MB / 3.775 = 252.1854305 seconds to download the file.
since bob starts at x = 0, he finishes at x = 461.2757576.
since alice starts at x = 142, she finishes at 142 + 252.1854305 = 394.1854305 seconds.
the equation for when they both downloaded the same number of bytes is -2.065 * x + 952 = -3.775 * (x - 142) + 952
the 952 on both sides of the equation cancels out and you are left with:
-2.065 * x = -3.775 * (x - 142)
simplify to get:
-2.065 * x = -3.775 * x + 536.05
add 3.775 * x to both sides of this equation to get:
1.71 * x = 536.05.
solve for x to get:
x = 536.05 / 1.71 = 313.4795322 seconds.
they will have both downloaded the same number of bytes 313.4795322 seconds after bob started.
since alice starts 142 seconds later than bob, they will have both downloaded the same number of bytes 313.4795322 - 142 = 171.4795322 seconds after alice started.
the number of bytes downloaded at that time will be 647.335234
the number of bytes left to be downloaded at that time is 952 - 647.335234 = 304.664766 bytes.
the graph of all this is shown below.
i'll be available to answer any questions you might have about this.
