document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162900>Question 1162900</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Edward takes 15 minutes longer than Kate does to make the 112-mile drive between two cities. Kate drives 8 miles an hour faster. How fast do Edward and Kate drive? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786800 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=786800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = time in hours it takes Kate to make the drive<BR>\n" );
document.write( "x+0.25 = time in hours it takes Edward to make the drive<BR>\n" );
document.write( "15 minutes = 1/4 hour = 0.25 hours\r<BR>\n" );
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document.write( "y = Edward's speed in miles per hour (mph)<BR>\n" );
document.write( "y+8 = Kate's speed in mph\r<BR>\n" );
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document.write( "For Edward,<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "112 = y*(x+0.25)<BR>\n" );
document.write( "which solves to <BR>\n" );
document.write( "y = 112/(x+0.25)\r<BR>\n" );
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document.write( "For Kate,<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "112 = (y+8)*x\r<BR>\n" );
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document.write( "Plug in y = 112/(x+0.25) and solve for x\r<BR>\n" );
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document.write( "112 = (y+8)*x<BR>\n" );
document.write( "112 = ( 112/(x+0.25) +8)*x<BR>\n" );
document.write( "112 = (112x)/(x+0.25) + 8x<BR>\n" );
document.write( "112-8x = (112x)/(x+0.25)<BR>\n" );
document.write( "(112-8x)(x+0.25) = 112x<BR>\n" );
document.write( "112x+28-8x^2-2x = 112x<BR>\n" );
document.write( "112x+28-8x^2-2x-112x = 0<BR>\n" );
document.write( "-8x^2-2x+28 = 0<BR>\n" );
document.write( "-2(4x^2+x-14) = 0<BR>\n" );
document.write( "4x^2+x-14 = 0\r<BR>\n" );
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document.write( "Use the quadratic formula to solve from here<BR>\n" );
document.write( "We have a = 4, b = 1, c = -14.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1.75 ALIGN=MIDDLE  ALT=\"x+=+1.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2 ALIGN=MIDDLE  ALT=\"x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Ignore the negative x value as a negative time value makes no sense.\r<BR>\n" );
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document.write( "x = 1.75 means it takes Kate 1.75 hours to make the drive<BR>\n" );
document.write( "1.75 hours = 1 hr + 0.75 hr = 1 hr + 45 min = 1 hr, 45 min\r<BR>\n" );
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document.write( "Add 15 minutes to this value to get 2 hours, which is the time it takes Edward to make the drive.\r<BR>\n" );
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document.write( "Once we know the time values, we can compute the speed values\r<BR>\n" );
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document.write( "speed = distance/time = 112/1.75 = 64 mph<BR>\n" );
document.write( "is Kate's speed\r<BR>\n" );
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document.write( "while, <BR>\n" );
document.write( "speed = distance/time = 112/2 = 56 mph<BR>\n" );
document.write( "is Edwards speed, exactly 8 mph less than Kate's speed.\r<BR>\n" );
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document.write( "=============================================<BR>\n" );
document.write( "Answers:\r<BR>\n" );
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document.write( "Kate's speed = 64 mph<BR>\n" );
document.write( "Edward's speed = 56 mph\r<BR>\n" );
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document.write( "</font> </SPAN>\n" );
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