document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=471037>Question 471037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> During the first part of a trip, a canoeist travels 83 miles at a certain speed. The canoeist travels 6 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 2 hours. What was the  on each part of the trip?<BR>\n" );
document.write( "The speed of the first part of the trip was ___mph.<BR>\n" );
document.write( "(Simplify your answer. Type an integer or a decimal. Round to the nearest hundredth.)<BR>\n" );
document.write( "The speed of the second part of the trip was __ mph.<BR>\n" );
document.write( "(Simplify your answer. Type an integer or a decimal. Round to the nearest hundredth.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #323110 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=323110\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> During the first part of a trip, a canoeist travels 83 miles at a certain speed.<BR>\n" );
document.write( " The canoeist travels 6 miles on the second part of the trip at a speed 5 mph slower.<BR>\n" );
document.write( " The total time for the trip is 2 hours.<BR>\n" );
document.write( " What was the on each part of the trip?<BR>\n" );
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document.write( "Let s = speed on the 1st part of the trip<BR>\n" );
document.write( "It says,\"the second part of the trip at a speed 5 mph slower.\", therefore<BR>\n" );
document.write( "(s-5) = speed on the 2nd part<BR>\n" );
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document.write( "Write a time equation, time = dist/speed<BR>\n" );
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document.write( "1st part time + 2nd part time = 2 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=83%2Fs ALIGN=MIDDLE  ALT=\"83%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%28%28s-5%29%29 ALIGN=MIDDLE  ALT=\"6%2F%28%28s-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
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document.write( "multiply by s(s-5), results:<BR>\n" );
document.write( "83(s-5) + 6s = 2s(s-5)<BR>\n" );
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document.write( "83s - 415 + 6s = 2s^2 - 10s<BR>\n" );
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document.write( "89s - 415 = 2s^2 - 10s<BR>\n" );
document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( "0 = 2s^2 - 10s - 89s + 415<BR>\n" );
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document.write( "2s^2 - 99s + 415 = 0<BR>\n" );
document.write( "Use the quadratic formula to find s<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%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( "In this equation: x=s; a=2; b=-99; c=415<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-%28-99%29+%2B-+sqrt%28-99%5E2-4%2A2%2A415+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"s+=+%28-%28-99%29+%2B-+sqrt%28-99%5E2-4%2A2%2A415+%29%29%2F%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%2899+%2B-+sqrt%289801-3320+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"s+=+%2899+%2B-+sqrt%289801-3320+%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%2899+%2B-+sqrt%286481%29%29%2F4+ ALIGN=MIDDLE  ALT=\"s+=+%2899+%2B-+sqrt%286481%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%2899+-+80.5%29%2F4+ ALIGN=MIDDLE  ALT=\"s+=+%2899+-+80.5%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18.5%2F4 ALIGN=MIDDLE  ALT=\"18.5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 4.625, obviously this is not the solution<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%2899+%2B+80.5%29%2F4+ ALIGN=MIDDLE  ALT=\"s+=+%2899+%2B+80.5%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=179.5%2F4 ALIGN=MIDDLE  ALT=\"179.5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 44.87 mph, is the speed on the 1st part of the trip<BR>\n" );
document.write( "and<BR>\n" );
document.write( "44.88 - 5 = 39.87 mph is the speed on the 2nd part<BR>\n" );
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document.write( "Check this by finding the actual time of each part<BR>\n" );
document.write( "83/44.87 = 1.85 hrs<BR>\n" );
document.write( " 6/39.87 = 0.15 hrs<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "total time: 2 hrs </SPAN>\n" );
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