document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=376588>Question 376588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> During the first part of a trip, a canoeist travels 71 miles at a certain speed. The canoeist travels 12 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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #267955 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=267955\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> During the first part of a trip, a canoeist travels 71 miles at a certain speed.<BR>\n" );
document.write( " The canoeist travels 12 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 5 hours. What was the speed on EACH part of the trip?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = speed for the 1st part of the trip<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-5) = speed on the 2nd part of the trip<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write time equation; time = dist/speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1st speed time + 2nd speed time = 5 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=71%2Fs ALIGN=MIDDLE  ALT=\"71%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28%28s-5%29%29 ALIGN=MIDDLE  ALT=\"12%2F%28%28s-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5<BR>\n" );
document.write( "Multiply by s(s-5) to clear the denominators, results:<BR>\n" );
document.write( "71(s-5) + 12s = 5s(s-5)<BR>\n" );
document.write( "71s - 355 + 12s = 5s^2 - 25s<BR>\n" );
document.write( "83s - 355 = 5s^2 - 25s<BR>\n" );
document.write( "0 = 5s^2 - 25s - 83s + 355<BR>\n" );
document.write( "5s^2 - 108s + 355 = 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( "Where x = s; a=5; b=-108; c=355<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-%28-108%29+%2B-+sqrt%28-108%5E2-4%2A5%2A355+%29%29%2F%282%2A5%29+ ALIGN=MIDDLE  ALT=\"s+=+%28-%28-108%29+%2B-+sqrt%28-108%5E2-4%2A5%2A355+%29%29%2F%282%2A5%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+=+%28108+%2B-+sqrt%2811664-7100+%29%29%2F10+ ALIGN=MIDDLE  ALT=\"s+=+%28108+%2B-+sqrt%2811664-7100+%29%29%2F10+\"   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+=+%28108+%2B-+sqrt%284564+%29%29%2F10+ ALIGN=MIDDLE  ALT=\"s+=+%28108+%2B-+sqrt%284564+%29%29%2F10+\"   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+=+%28108+%2B+67.557%29%2F10+ ALIGN=MIDDLE  ALT=\"s+=+%28108+%2B+67.557%29%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=175.557%2F10 ALIGN=MIDDLE  ALT=\"175.557%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 17.5557<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28108+-+67.557%29%2F10+ ALIGN=MIDDLE  ALT=\"s+=+%28108+-+67.557%29%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40.443%2F10 ALIGN=MIDDLE  ALT=\"40.443%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 4.0443<BR>\n" );
document.write( ":<BR>\n" );
document.write( "s = 17.5557 mph is the only reasonable speed for the 1st part of the trip<BR>\n" );
document.write( "and<BR>\n" );
document.write( "17.5557 - 5 = 12.5557 mph is the speed on the 2nd part of the trip<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if this is true, find the time at each speed<BR>\n" );
document.write( "71/17.5557 = 4.044 hrs<BR>\n" );
document.write( "12/12.5557 = .9557<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "total time: 4.9997 ~ 5 hrs </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );