document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=526139>Question 526139</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please explain to me step by step how to complete this problem? I am able to get to the part where you simplify but am not able to get no farther.<BR>\n" );
document.write( "During the first part of a trip, a canoeist travels 91 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( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #348350 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=348350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> During the first part of a trip, a canoeist travels 61 miles at a certain speed.<BR>\n" );
document.write( " The canoeist travels 2 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 3 hours. What was the speed on each part of the trip?<BR>\n" );
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document.write( "Let s = the speed for the 1st 61 mi<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-5) = the speed for the last 2 mi<BR>\n" );
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document.write( "Write a time equation, time = dist/speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "faster time + slower time = 3 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61%2Fs ALIGN=MIDDLE  ALT=\"61%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28s-5%29 ALIGN=MIDDLE  ALT=\"2%2F%28s-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
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document.write( "multiply by s(s-5), results:<BR>\n" );
document.write( "61(s-5) + 2s = 3s(s-5)<BR>\n" );
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document.write( "61s - 305 + 2s = 3s^2 - 15s<BR>\n" );
document.write( "63s - 305 = 3s^2 - 15s<BR>\n" );
document.write( "Arrange as a quadratic equation on the right<BR>\n" );
document.write( "0 = 3s^2 - 15s - 63s + 305<BR>\n" );
document.write( "3s^2 - 78s + 305 = 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 problem, a=3, b=-78, c=305, x=s<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-%28-78%29+%2B-+sqrt%28-78%5E2-4%2A3%2A305+%29%29%2F%282%2A3%29+ ALIGN=MIDDLE  ALT=\"s+=+%28-%28-78%29+%2B-+sqrt%28-78%5E2-4%2A3%2A305+%29%29%2F%282%2A3%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+=+%2878+%2B-+sqrt%286084-3660+%29%29%2F6+ ALIGN=MIDDLE  ALT=\"s+=+%2878+%2B-+sqrt%286084-3660+%29%29%2F6+\"   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+=+%2878+%2B-+sqrt%282424%29%29%2F6+ ALIGN=MIDDLE  ALT=\"s+=+%2878+%2B-+sqrt%282424%29%29%2F6+\"   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+=+%2878+%2B+49.234%29%2F6+ ALIGN=MIDDLE  ALT=\"s+=+%2878+%2B+49.234%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=127.234%2F6 ALIGN=MIDDLE  ALT=\"127.234%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 21.206  <BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%2878+-+49.234%29%2F6+ ALIGN=MIDDLE  ALT=\"s+=+%2878+-+49.234%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28.766%2F6 ALIGN=MIDDLE  ALT=\"28.766%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 4.794<BR>\n" );
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document.write( "Obviously the only reasonable solution:<BR>\n" );
document.write( "s = 21.206 mph on the first 61 mi<BR>\n" );
document.write( "and<BR>\n" );
document.write( " 16.206 mph on the last two miles <BR>\n" );
document.write( ":<BR>\n" );
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document.write( "See if that check out, find the actual time of each<BR>\n" );
document.write( "61/21.206 = 2.876 hrs<BR>\n" );
document.write( "2/16.206  =  .123 hrs<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "total time: 3.0 hrs  </SPAN>\n" );
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