document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1060571>Question 1060571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. A ship leaves a harbor sailing at 28 mph. A plane leaves 6-1/2 hours later. At what rate must it fly to overtake the ship in an hour and 15 min.? \r<BR>\n" );
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document.write( "2. A man flew to another city for a meeting at a rate of 260 mph. He returned by train at a rate of <BR>\n" );
document.write( "60 mph. If his total travel time was 4 hours, what was his flying time? \r<BR>\n" );
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document.write( "I am a home school mom trying to help my daughter with these 2 problems. I would appreciate any help. Thank you very much! Tara  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #675497 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=675497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> These problems are in the category of<BR>\n" );
document.write( "\" related rate \" problems. For word problems,<BR>\n" );
document.write( "it's very important to identify their category.<BR>\n" );
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document.write( "(1)<BR>\n" );
document.write( "What is the head start in miles for the ship?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B1%5D+=+28%2A6.5+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+=+28%2A6.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B1%5D+=+182+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+=+182+\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the distance in miles the plane <BR>\n" );
document.write( "travels until it catches up with the ship<BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+ ALIGN=MIDDLE  ALT=\"+s+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the flying speed of the plane so <BR>\n" );
document.write( "that the plane catches up with the ship in<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.25+ ALIGN=MIDDLE  ALT=\"+1.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
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document.write( "Equation for the plane:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+s%2A1.25+ ALIGN=MIDDLE  ALT=\"+d+=+s%2A1.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation for the ship:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+-+182+=+28%2A1.25+ ALIGN=MIDDLE  ALT=\"+d+-+182+=+28%2A1.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Substitute (1) into (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.25s+-+182+=+28%2A1.25+ ALIGN=MIDDLE  ALT=\"+1.25s+-+182+=+28%2A1.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.25s+=+35+%2B+182+ ALIGN=MIDDLE  ALT=\"+1.25s+=+35+%2B+182+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.25s+=+217+ ALIGN=MIDDLE  ALT=\"+1.25s+=+217+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+173.6+ ALIGN=MIDDLE  ALT=\"+s+=+173.6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The plane's flying rate is 173.6 mi/hr<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "check the answer:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+s%2A1.25+ ALIGN=MIDDLE  ALT=\"+d+=+s%2A1.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+173.6%2A1.25+ ALIGN=MIDDLE  ALT=\"+d+=+173.6%2A1.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+217+ ALIGN=MIDDLE  ALT=\"+d+=+217+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+-+182+=+28%2A1.25+ ALIGN=MIDDLE  ALT=\"+d+-+182+=+28%2A1.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+217+-+182+=+28%2A1.25+ ALIGN=MIDDLE  ALT=\"+217+-+182+=+28%2A1.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+35+=+35+ ALIGN=MIDDLE  ALT=\"+35+=+35+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "(2)<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = his flying time in hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+-+t+ ALIGN=MIDDLE  ALT=\"+4+-+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = his time traveling by train<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the distance to the city<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "Equation for traveling by train:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+60%2A%28+4+-+t+%29+ ALIGN=MIDDLE  ALT=\"+d+=+60%2A%28+4+-+t+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation for flying:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+260t+ ALIGN=MIDDLE  ALT=\"+d+=+260t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "substitute (2) into (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+260t+=+60%2A%28+4+-+t+%29+ ALIGN=MIDDLE  ALT=\"+260t+=+60%2A%28+4+-+t+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+260t+=+240+-+60t+ ALIGN=MIDDLE  ALT=\"+260t+=+240+-+60t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+320t+=+240+ ALIGN=MIDDLE  ALT=\"+320t+=+240+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+.75+ ALIGN=MIDDLE  ALT=\"+t+=+.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "His flying time is 3/4 of an hour, or 45 minutes<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "check the answer<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+260t+ ALIGN=MIDDLE  ALT=\"+d+=+260t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+260%2A.75+ ALIGN=MIDDLE  ALT=\"+d+=+260%2A.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+195+ ALIGN=MIDDLE  ALT=\"+d+=+195+\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+60%2A%28+4+-+t+%29+ ALIGN=MIDDLE  ALT=\"+d+=+60%2A%28+4+-+t+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+60%2A%28+4+-+.75+%29+ ALIGN=MIDDLE  ALT=\"+d+=+60%2A%28+4+-+.75+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+60%2A3.25+ ALIGN=MIDDLE  ALT=\"+d+=+60%2A3.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+195+ ALIGN=MIDDLE  ALT=\"+d+=+195+\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "OK<BR>\n" );
document.write( "Hope this helps\r<BR>\n" );
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document.write( " </SPAN>\n" );
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