document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=833439>Question 833439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a bicycle race over a 20 km route, Danny finished 8 minutes ahead of John. Danny pedaled 5 km per hour faster than John. What was Danny's rate </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #502536 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39627)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=502536\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Uniform rates for travel, using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%2AT=D ALIGN=MIDDLE  ALT=\"R%2AT=D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "This example is in kilometers and hours.<BR>\n" );
document.write( "8 minutes is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F60=2%2F15 ALIGN=MIDDLE  ALT=\"8%2F60=2%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > hour<BR>\n" );
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document.write( "Let t = time for John to finish the race\r<BR>\n" );
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document.write( "______________speed_____________time_______________distance(km)<BR>\n" );
document.write( "Danny_________(___)_____________t-8/60_____________20<BR>\n" );
document.write( "John_________(____)______________t_________________20\r<BR>\n" );
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document.write( "Danny is at a rate r+5, if John went at a rate of r.  The rates are unknown.<BR>\n" );
document.write( "This and also reducing the time expression for Danny,...\r<BR>\n" );
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document.write( "______________speed_____________time_______________distance(km)<BR>\n" );
document.write( "Danny_________(r+5)_____________t-2/15_____________20<BR>\n" );
document.write( "John_________(r)_________________t_________________20\r<BR>\n" );
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document.write( "A rate*time=distance equation can be made for each of Danny and John.\r<BR>\n" );
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document.write( "John: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28rt=20%29 ALIGN=MIDDLE  ALT=\"highlight_green%28rt=20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which can also be used as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28t=20%2Fr%29 ALIGN=MIDDLE  ALT=\"highlight_green%28t=20%2Fr%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Danny:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2B5%29%28t-2%2F15%29=20 ALIGN=MIDDLE  ALT=\"%28r%2B5%29%28t-2%2F15%29=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rt%2B5t-2r%2F15-2%2F3=20 ALIGN=MIDDLE  ALT=\"rt%2B5t-2r%2F15-2%2F3=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting with John's equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2B5t-2r%2F15-2%2F3=20 ALIGN=MIDDLE  ALT=\"20%2B5t-2r%2F15-2%2F3=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5t-2r%2F15-2%2F3=0 ALIGN=MIDDLE  ALT=\"5t-2r%2F15-2%2F3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply members by 15 to clear the denominators<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75t-2r-10=0 ALIGN=MIDDLE  ALT=\"75t-2r-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Make use of John's equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2820%2Fr%29-2r-10=0 ALIGN=MIDDLE  ALT=\"75%2820%2Fr%29-2r-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500%2Fr-2r-10=0 ALIGN=MIDDLE  ALT=\"1500%2Fr-2r-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500-2r%5E2-10r=0 ALIGN=MIDDLE  ALT=\"1500-2r%5E2-10r=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2r%5E2-10r%2B1500=0 ALIGN=MIDDLE  ALT=\"-2r%5E2-10r%2B1500=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28r%5E2%2B5r-750=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%28r%5E2%2B5r-750=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >----Quadratic equation in r, the rate for John.<BR>\n" );
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document.write( "Use the * general solution to a quadratic equation to solve for r, even through the question really just asks for Danny's rate; both rates are given a relationship in the description.<BR>\n" );
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document.write( "* The quadratic expression on the left hand side is factorable, so you might be able to explore the factorizations of 750, but you will find that the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28r-30%29%28r%2B25%29=0%29 ALIGN=MIDDLE  ALT=\"highlight%28%28r-30%29%28r%2B25%29=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The meaningful answer is, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28r=30%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28r=30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This means, Danny's rate was 35 kilometers per hour. </SPAN>\n" );
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