document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162664>Question 162664</A>: <I><SPAN STYLE=\"word-break: break-all;\"> During the first part of a trip, a canoeist travels 69 miles at a certain speed. The canoeist travels 2 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 3 hrs. 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 #119893 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=119893\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> During the first part of a trip, a canoeist travels 69 miles at a certain speed. The canoeist travels 2 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 3 hrs. What was the speed on each part of the trip?<BR>\n" );
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document.write( "Canoing that far in 3 hrs is a fantasy, but anyway:<BR>\n" );
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document.write( "Let s = speed on the 69 miles<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-5) = speed on the last to miles of the trip<BR>\n" );
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document.write( "Write a time equation: Time = dist/speed<BR>\n" );
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document.write( "69 mi time + 2 mi time = 3 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=69%2Fs ALIGN=MIDDLE  ALT=\"69%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28%28s-5%29%29 ALIGN=MIDDLE  ALT=\"2%2F%28%28s-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
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document.write( "Multiply equation by s(s-5), results:<BR>\n" );
document.write( "69(s-5) + 2s = 3s(s-5)<BR>\n" );
document.write( "69s - 345 + 2s = 3s^2 - 15s<BR>\n" );
document.write( "71s - 345 = 3s^2 - 15s<BR>\n" );
document.write( "0 = 3s^2 - 15s = 71s + 345 <BR>\n" );
document.write( "A quadratic equation:<BR>\n" );
document.write( "3s^2 - 86s + 345 = 0 <BR>\n" );
document.write( "Use the quadratic formula to solve this<BR>\n" );
document.write( "The solution that makes sense is s ~ 23.84 mph for the 1st 69mi<BR>\n" );
document.write( "and<BR>\n" );
document.write( "23.84 - 5 = 18.84 mph for the last two mi<BR>\n" );
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document.write( "Check solution by finding the times at each speed<BR>\n" );
document.write( "69/23.84 = 2.89 hrs<BR>\n" );
document.write( "2/18.84 = .106 hr<BR>\n" );
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document.write( "total time 2.996 ~ 3 hrs<BR>\n" );
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document.write( "I suspect there may be a typo in this as written here, but the method should<BR>\n" );
document.write( "help you.  </SPAN>\n" );
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