document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6597>Question 6597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help on solving this word problem:\r<BR>\n" );
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document.write( "Trisha ran to the park and then walked home.  It took her 1/2 hours to get to the park and 1 hour adn 20 minutes to get home.  If she runs 5 miles an hour faster then she walks, how far does she live from the park? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3597 by </B><A HREF=/tutors/aboutme.mpl?userid=prince_abubu><B>prince_abubu(198)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=prince_abubu><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=3597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We'll work with the equation r * t = d. In this situation, we have two different rates and two different times but the same distance. Let's label some variables:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Bw%5D+ ALIGN=MIDDLE  ALT=\"+r%5Bw%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = walking speed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Br%5D+ ALIGN=MIDDLE  ALT=\"+r%5Br%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = running speed, which really is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Bw%5D+%2B+5+ ALIGN=MIDDLE  ALT=\"+r%5Bw%5D+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5Bw%5D+ ALIGN=MIDDLE  ALT=\"+t%5Bw%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time it took her to run to the park, which is 1/2 hour<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5Br%5D+ ALIGN=MIDDLE  ALT=\"+t%5Br%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time it took her to walk, which is 1 1/3 hours (that's 1 hour and 20 minutes in fraction form)\r<BR>\n" );
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document.write( "Since she will walk and run the same distance, we can say\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Bw%5D%2At%5Bw%5D+=+r%5Br%5D%2At%5Br%5D+ ALIGN=MIDDLE  ALT=\"+r%5Bw%5D%2At%5Bw%5D+=+r%5Br%5D%2At%5Br%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- We are actually interested in finding the distance, but in this case, we have to find the rates first.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Bw%5D%2A%284%2F3%29+=+%28r%5Bw%5D%2B5%29%2A%281%2F2%29+ ALIGN=MIDDLE  ALT=\"+r%5Bw%5D%2A%284%2F3%29+=+%28r%5Bw%5D%2B5%29%2A%281%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <----- We did some substitutions and turned 1 1/3 to an improper fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4r%5Bw%5D+=+3%28r%5Bw%5D%2B5%29%281%2F2%29+ ALIGN=MIDDLE  ALT=\"+4r%5Bw%5D+=+3%28r%5Bw%5D%2B5%29%281%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- multiply both sides by 3 to get rid of the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8r%5Bw%5D+=+3%28r%5Bw%5D+%2B+5%29+ ALIGN=MIDDLE  ALT=\"+8r%5Bw%5D+=+3%28r%5Bw%5D+%2B+5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- multiply both sides by 2 to get rid of the other fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8r%5Bw%5D+=+3r%5Bw%5D+%2B+15+ ALIGN=MIDDLE  ALT=\"+8r%5Bw%5D+=+3r%5Bw%5D+%2B+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- expand using distributive property for the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Bw%5D+=+3+ ALIGN=MIDDLE  ALT=\"+r%5Bw%5D+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <----- Her walking speed was 3 miles per hour. Since it took her 1 hour and 20 minutes (4/3 of an hour) to walk at 3 miles per hour, the distance would've been r*t = (3)*(4/3) = 4 miles. </SPAN>\n" );
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