document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177907>Question 1177907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At 5:12:40 PM Bob starts downloading a 952MB media file at 16.5Mbps.\r<BR>\n" );
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document.write( "At 5:15:02 PM Alice starts downloading the same media file at 30.2 Mbps.\r<BR>\n" );
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document.write( "a) How many seconds will it take for Bob and Alice to download the file?\r<BR>\n" );
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document.write( "b) Plot the graph of downloaded filesize vs. time for both Bob and Alice.\r<BR>\n" );
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document.write( "c) How many seconds will it take for Alice have exactly the same partially downloaded filesize as Bob?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807086 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=807086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the straight line eqution to use is:\r<BR>\n" );
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document.write( "y = mx + b<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept.\r<BR>\n" );
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document.write( "x = 0 seconds at 15:12:40 pm.<BR>\n" );
document.write( "x = 142 seconds at 15:15:02 pm.\r<BR>\n" );
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document.write( "bob downloads at 16.5 megabits per second.<BR>\n" );
document.write( "alice downloads at 30.2 megabits per second.\r<BR>\n" );
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document.write( "the file size is 952 megabytes.<BR>\n" );
document.write( "one byte is equal to 8 bits.\r<BR>\n" );
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document.write( "downloading at 16.5 megabits per second / 8 = 2.0625 megabytes per second.<BR>\n" );
document.write( "downloading at 30.2 megabits per second / 8 = 3.775 megabytes per second.\r<BR>\n" );
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document.write( "the straight line equation for bob is y = -2.0625 * x + 952<BR>\n" );
document.write( "the straight line equation for alice is y = 3.775 * (x - 142) + 952.\r<BR>\n" );
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document.write( "the equation for alice uses (x - 142) rather than x because alice starts 142 seconds after bob.\r<BR>\n" );
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document.write( "the calculations for determining that alice starts 142 seconds after bob are:<BR>\n" );
document.write( "5:15:02 minus 5:12:40 = 5:14:62 minus 5:12:40 = 0:2:22 = 0:0:142.<BR>\n" );
document.write( "0:0:142 is equal to 142 seconds.\r<BR>\n" );
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document.write( "for bob, 952 MB / 2.0625 = 461.2757576 seconds to download the file.<BR>\n" );
document.write( "for alice, 952 MB / 3.775 = 252.1854305 seconds to download the file.\r<BR>\n" );
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document.write( "since bob starts at x = 0, he finishes at x = 461.2757576.\r<BR>\n" );
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document.write( "since alice starts at x = 142, she finishes at 142 + 252.1854305 = 394.1854305 seconds.\r<BR>\n" );
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document.write( "the equation for when they both downloaded the same number of bytes is -2.065 * x + 952 = -3.775 * (x - 142) + 952<BR>\n" );
document.write( "the 952 on both sides of the equation cancels out and you are left with:<BR>\n" );
document.write( "-2.065 * x = -3.775 * (x - 142)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "-2.065 * x = -3.775 * x + 536.05<BR>\n" );
document.write( "add 3.775 * x to both sides of this equation to get:<BR>\n" );
document.write( "1.71 * x = 536.05.<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 536.05 / 1.71 = 313.4795322 seconds.\r<BR>\n" );
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document.write( "they will have both downloaded the same number of bytes 313.4795322 seconds after bob started.<BR>\n" );
document.write( "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.\r<BR>\n" );
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document.write( "the number of bytes downloaded at that time will be 647.335234<BR>\n" );
document.write( "the number of bytes left to be downloaded at that time is 952 - 647.335234 = 304.664766 bytes.\r<BR>\n" );
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document.write( "the graph of all this is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/040101.jpg\">\r<BR>\n" );
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document.write( "i'll be available to answer any questions you might have about this.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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