document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=426723>Question 426723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a bicyclist leaves a point and then a car leaves the same point 2 hours later going 12mph faster. After 90 miles the car catches the bicyclist. Find the speed of both the car and the bicyclist. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296829 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=296829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a bicyclist leaves a point and then a car leaves the same point 2 hours later going 12mph faster.<BR>\n" );
document.write( " After 90 miles the car catches the bicyclist.<BR>\n" );
document.write( " Find the speed of both the car and the bicyclist.<BR>\n" );
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document.write( "Let s = the bike speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+12) = the car speed<BR>\n" );
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document.write( "Write a time equation: time = dist/speed<BR>\n" );
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document.write( "Bike time = Car time + 2 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2Fs ALIGN=MIDDLE  ALT=\"90%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2F%28%28s%2B12%29%29 ALIGN=MIDDLE  ALT=\"90%2F%28%28s%2B12%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2<BR>\n" );
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document.write( "Multiply by s(s+12), results<BR>\n" );
document.write( "90(s+12) = 90s + 2s(s+12)<BR>\n" );
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document.write( "90s + 1080 = 90s + 2s^2 + 24s<BR>\n" );
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document.write( "Arrange as a quadratic equation on the right<BR>\n" );
document.write( "0 = 90s - 90s + 2s^2 + 24s - 1080<BR>\n" );
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document.write( "2s^2 + 24s - 1080 = 0<BR>\n" );
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document.write( "Simplify,divide by 2<BR>\n" );
document.write( "s^2 + 12s - 540 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(s-18)(s+30) = 0<BR>\n" );
document.write( "the positive solution<BR>\n" );
document.write( "s = 18 mph is the bike speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "18 + 12 = 30 mph is the car's<BR>\n" );
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document.write( "Check solution by finding the actual travel time of each<BR>\n" );
document.write( "90/18 = 5 hrs<BR>\n" );
document.write( "90/30 = 3 hrs<BR>\n" );
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document.write( "a diff of 2 hrs </SPAN>\n" );
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