document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130883>Question 130883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> During the first part of a trip, a canoeist travels 75 miles at a certain speed.  The canoeist travels 24 miles on the second part of the trip at a speed 5 mph slower.  The total time for the trip is 5 hours.  What was the speed on each part of the trip?\r<BR>\n" );
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document.write( "The speed on the first part of the trip was ____  mph.\r<BR>\n" );
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document.write( "The speed on the second part of the trip was ____ mph.\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 #95740 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=95740\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Distance(d)=Rate(r) times Time(t) or d=rt; r=d/t and t=d/r\r<BR>\n" );
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document.write( "Let r=speed for first part of trip<BR>\n" );
document.write( "Then r-5=speed on second part of trip\r<BR>\n" );
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document.write( "Time required for first part of trip= d/r=75/r<BR>\n" );
document.write( "Time required for second part of trip=d/r=24/(r-5)\r<BR>\n" );
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document.write( "Now we are told that the sum of the above two times equals 5 hours, so:\r<BR>\n" );
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document.write( "75/r+24/(r-5)=5  multiply each term by r(r-5)\r<BR>\n" );
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document.write( "75(r-5)+24r=5r(r-5)  get rid of parens\r<BR>\n" );
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document.write( "75r-375+24r=5r^2-25r  subtract 5r^2 from and add 25r to both sides<BR>\n" );
document.write( "75r-375+24r-5r^2+25r=5r^2-5r^2-25r+25r  collect like terms\r<BR>\n" );
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document.write( "-5r^2+124r-375=0  multiply each term by -1\r<BR>\n" );
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document.write( "5r^2-124r+375=0  quadratic in standard form.  Solve using quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28124+%2B-+sqrt%28+%28-124%29%5E2-4%2A5%2A%28-375%29+%29%29%2F%282%2A5%29+ ALIGN=MIDDLE  ALT=\"r+=+%28124+%2B-+sqrt%28+%28-124%29%5E2-4%2A5%2A%28-375%29+%29%29%2F%282%2A5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28124+%2B-+sqrt%287876+%29%29%2F%2810%29+ ALIGN=MIDDLE  ALT=\"r+=+%28124+%2B-+sqrt%287876+%29%29%2F%2810%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28124+%2B-88.75%29%2F%2810%29+ ALIGN=MIDDLE  ALT=\"r+=+%28124+%2B-88.75%29%2F%2810%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28124+%2B88.75+%29%2F%2810%29+ ALIGN=MIDDLE  ALT=\"r+=+%28124+%2B88.75+%29%2F%2810%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+21.275 ALIGN=MIDDLE  ALT=\"r+=+21.275\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph------speed on first part of trip<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r-5=21.275-5=16.275 ALIGN=MIDDLE  ALT=\"r-5=21.275-5=16.275\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph---speed on second part of trip\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28124+-88.75+%29%2F%2810%29+ ALIGN=MIDDLE  ALT=\"r+=+%28124+-88.75+%29%2F%2810%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+3.525 ALIGN=MIDDLE  ALT=\"r+=+3.525\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph--------------speed on second part of trip (NO!!!)<BR>\n" );
document.write( "r-5=3.535-5=NEGATIVE VALUE  NO GOOD!!!!\r<BR>\n" );
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document.write( "CK\r<BR>\n" );
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document.write( "75/21.275 + 24/16.275=5<BR>\n" );
document.write( "3.525+1.474=5<BR>\n" );
document.write( "4.999999--~~~~5\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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