document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=600979>Question 600979</A>: <I><SPAN STYLE=\"word-break: break-all;\"> During the first part of a trip, a canoeist travels 45 miles at a certain speed. The canoeist travels 20 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 2 hrs. What was the speed on each part of the trip?<BR>\n" );
document.write( "The speed on the first part of the trip was _______ mph. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #379598 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=379598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> During the first part of a trip, a canoeist travels 45 miles at a certain speed.<BR>\n" );
document.write( " The canoeist travels 20 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 hrs. What was the speed on each part of the trip?<BR>\n" );
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document.write( "Let s = speed the first part of the trip<BR>\n" );
document.write( "and<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=45%2Fs ALIGN=MIDDLE  ALT=\"45%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F%28%28s-5%29%29 ALIGN=MIDDLE  ALT=\"20%2F%28%28s-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
document.write( "multiply by s(s-5) to clear the denominators, results:<BR>\n" );
document.write( "45(s-5) + 20s = 2s(s-5)<BR>\n" );
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document.write( "45s - 225 + 20s = 2s^2 - 10s<BR>\n" );
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document.write( "65s - 225 = 2s^2 - 10s<BR>\n" );
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document.write( "0 = 2s^2 - 10s - 65s + 225 <BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "2s^2 - 75s + 225 = 0<BR>\n" );
document.write( "Use the quadratic formula to fins 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=-75; c=225<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-%28-75%29+%2B-+sqrt%28-75%5E2-4%2A2%2A225+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"s+=+%28-%28-75%29+%2B-+sqrt%28-75%5E2-4%2A2%2A225+%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+=+%2875+%2B-+sqrt%285625-1800+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"s+=+%2875+%2B-+sqrt%285625-1800+%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+=+%2875+%2B-+sqrt%283825+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"s+=+%2875+%2B-+sqrt%283825+%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions, but only this one makes sense.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%2875+%2B+61.85%29%2F4+ ALIGN=MIDDLE  ALT=\"s+=+%2875+%2B+61.85%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=136.84%2F4 ALIGN=MIDDLE  ALT=\"136.84%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 34.2 mph on the 1st part of the trip<BR>\n" );
document.write( "and<BR>\n" );
document.write( "34.2 - 5 = 29.2 mph on the 2nd part<BR>\n" );
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document.write( "Let's see if this checks out, find sum of the times at each speed<BR>\n" );
document.write( "45/34.2 = 1.3158 hrs at 34.2 mph<BR>\n" );
document.write( "20/29.2 = 0.6849 hrs at 29.2 mph<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "tot time: 2.0007 hrs which is the total time<BR>\n" );
document.write( " </SPAN>\n" );
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