document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=806891>Question 806891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> during the first part of a trip a canoeist travels 18 miles at a certain speed. The canoeist travels 4 miles on the second part of the trip at a speed of 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 #486143 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=486143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> During the first part of a trip a canoeist travels 18 miles at a certain speed.<BR>\n" );
document.write( " The canoeist travels 4 miles on the second part of the trip at a speed of 5 mph slower.<BR>\n" );
document.write( " The total time for the trip is 3 hrs.<BR>\n" );
document.write( " What was the speed on each part of the trip?<BR>\n" );
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document.write( "Let s = speed on the first part of the trip<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-5) = speed on the last part<BR>\n" );
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document.write( "Write a time equation; time = dist/speed:<BR>\n" );
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document.write( "Time for the 1st 18 mi + time for the last 4 mi = 3 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Fs ALIGN=MIDDLE  ALT=\"18%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28s-5%29 ALIGN=MIDDLE  ALT=\"4%2F%28s-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
document.write( "multiply by s(s-5), cancel the denominators, resulting in:<BR>\n" );
document.write( "18(s-5) + 4s = 3s(s-5)<BR>\n" );
document.write( "18s - 90 + 4s = 3s^2 - 15s<BR>\n" );
document.write( "22s - 90 = 3s^2 - 15s<BR>\n" );
document.write( "a quadratic equation<BR>\n" );
document.write( "0 = 3s^2 - 15s - 22s + 90<BR>\n" );
document.write( "3s^2 - 37s + 90 = 0<BR>\n" );
document.write( "We can us the quadratic formula, but this will factor to<BR>\n" );
document.write( "(3s-10)(s-9) = 0<BR>\n" );
document.write( "s = 9 mph on the 1st part of the trip is the reasonable solution<BR>\n" );
document.write( "then<BR>\n" );
document.write( "9-5 = 4 mph is the speed on the last part<BR>\n" );
document.write( ":<BR>\n" );
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document.write( "Check this, find the time at each speed<BR>\n" );
document.write( "18/9 = 2 hrs<BR>\n" );
document.write( "4/4 = 1 hr<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "total 3 hrs </SPAN>\n" );
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