document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129829>Question 129829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3) During the first part of a trip, a canoeist travels 82 miles at a certain speed. The canoeist travels 19 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?\r<BR>\n" );
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document.write( "The speed on the first part of the trip was _______ mph.<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 #94798 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=94798\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's use the formula d=r*t\r<BR>\n" );
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document.write( "Since \"a canoeist travels 82 miles at a certain speed\", this means that our first equation is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=82=rt%5B1%5D ALIGN=MIDDLE  ALT=\"82=rt%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice how I plugged in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=82 ALIGN=MIDDLE  ALT=\"d=82\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=t%5B1%5D ALIGN=MIDDLE  ALT=\"t=t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, since the \"canoeist travels 19 miles on the second part of the trip at a speed 5 mph slower\", the second equation is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19=%28r-5%29t%5B2%5D ALIGN=MIDDLE  ALT=\"19=%28r-5%29t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice how I plugged in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=19 ALIGN=MIDDLE  ALT=\"d=19\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=t%5B2%5D ALIGN=MIDDLE  ALT=\"t=t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Also, I replaced r with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r-5 ALIGN=MIDDLE  ALT=\"r-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since the canoeist traveled 5 mph slower)\r<BR>\n" );
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document.write( "Finally, because the \"total time for the trip is 3 hrs\", the third equation is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D%2Bt%5B2%5D=3 ALIGN=MIDDLE  ALT=\"t%5B1%5D%2Bt%5B2%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have the three equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19=%28r-5%29t%5B2%5D ALIGN=MIDDLE  ALT=\"19=%28r-5%29t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D%2Bt%5B2%5D=3 ALIGN=MIDDLE  ALT=\"t%5B1%5D%2Bt%5B2%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "--------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=82=rt%5B1%5D ALIGN=MIDDLE  ALT=\"82=rt%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=82%2Fr=t%5B1%5D ALIGN=MIDDLE  ALT=\"82%2Fr=t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Divide both sides by r  to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D ALIGN=MIDDLE  ALT=\"t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D=82%2Fr ALIGN=MIDDLE  ALT=\"t%5B1%5D=82%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Rearrange the equation\r<BR>\n" );
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document.write( "--------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19=%28r-5%29t%5B2%5D ALIGN=MIDDLE  ALT=\"19=%28r-5%29t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2F%28r-5%29=t%5B2%5D ALIGN=MIDDLE  ALT=\"19%2F%28r-5%29=t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r-5 ALIGN=MIDDLE  ALT=\"r-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D ALIGN=MIDDLE  ALT=\"t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D=19%2F%28r-5%29 ALIGN=MIDDLE  ALT=\"t%5B2%5D=19%2F%28r-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Rearrange the equation\r<BR>\n" );
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document.write( "------------------------------\r<BR>\n" );
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document.write( "Now let's focus on the third equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D%2Bt%5B2%5D=3 ALIGN=MIDDLE  ALT=\"t%5B1%5D%2Bt%5B2%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=82%2Fr%2B19%2F%28r-5%29=3 ALIGN=MIDDLE  ALT=\"82%2Fr%2B19%2F%28r-5%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D=82%2Fr ALIGN=MIDDLE  ALT=\"t%5B1%5D=82%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D=19%2F%28r-5%29 ALIGN=MIDDLE  ALT=\"t%5B2%5D=19%2F%28r-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the third equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28r-5%29%2882%2Fr%2B19%2F%28r-5%29%29=r%28r-5%29%283%29 ALIGN=MIDDLE  ALT=\"r%28r-5%29%2882%2Fr%2B19%2F%28r-5%29%29=r%28r-5%29%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28r-5%29 ALIGN=MIDDLE  ALT=\"r%28r-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=82%28r-5%29%2B19r=3r%28r-5%29 ALIGN=MIDDLE  ALT=\"82%28r-5%29%2B19r=3r%28r-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=82r-410%2B19r=3r%5E2-15r ALIGN=MIDDLE  ALT=\"82r-410%2B19r=3r%5E2-15r\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute again \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=82r-410%2B19r-3r%5E2%2B15r=0 ALIGN=MIDDLE  ALT=\"82r-410%2B19r-3r%5E2%2B15r=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract 3r^2 from both sides.  Add 15r to both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3r%5E2%2B116r-410=0 ALIGN=MIDDLE  ALT=\"-3r%5E2%2B116r-410=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "So after using the quadratic formula or a calculator, we get the solutions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=3.93492 ALIGN=MIDDLE  ALT=\"r=3.93492\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=34.73175 ALIGN=MIDDLE  ALT=\"r=34.73175\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, since you cannot take 5 mph away from 3.93 mph (you'll get a negative answer if you do), this means that our only answer is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=34.73175 ALIGN=MIDDLE  ALT=\"r=34.73175\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the speed on the first part of the trip was about 34.73 mph<BR>\n" );
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