document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121905>Question 121905</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395352495/algebrahomeworkh>Algebra: structure and method: Book 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Dale hikes 15km up a mountain trail. Her return trip on the same trail takes 30 mins less because she is able to increase her speed by 1 km/h. How long does it take her to climb up and down the mountain? I REALLY NEED HELP WITH THIS!!! The answer is 5 1/2 hours, but I do not know how to get there. I am also supposed to make a chart, but I think I can do that with the info you give me.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89495 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89495\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember the formula, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The rate going up is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=15%2Ft ALIGN=MIDDLE  ALT=\"r=15%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the rate coming down is 1 km/h faster and the time is a half hour less for the same 15 km, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2B1=15%2F%28t-0.5%29 ALIGN=MIDDLE  ALT=\"r%2B1=15%2F%28t-0.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve the second equation for r by adding -1 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%2815%2F%28t-0.5%29%29-1 ALIGN=MIDDLE  ALT=\"r=%2815%2F%28t-0.5%29%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > giving us a second expression for r in terms of t.\r<BR>\n" );
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document.write( "Now since r = r, we can say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Ft=%2815%2F%28t-0.5%29%29-1 ALIGN=MIDDLE  ALT=\"15%2Ft=%2815%2F%28t-0.5%29%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The LCD is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%28t-0.5%29 ALIGN=MIDDLE  ALT=\"t%28t-0.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%28t-0.5%29%2Ft%28t-.05%29%29=%2815t%2Ft%28t-0.5%29%29-%28t%28t-0.5%29%2Ft%28t-0.5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now put everything on the left:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%28t-0.5%29-%2815t%29%2B%28t%28t-0.5%29%29%29%2Ft%28t-0.5%29=0 ALIGN=MIDDLE  ALT=\"%2815%28t-0.5%29-%2815t%29%2B%28t%28t-0.5%29%29%29%2Ft%28t-0.5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute, expand, and collect terms in the numerator but leave the denominator alone:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t%5E2-0.5t-7.5%29%2Ft%28t-0.5%29=0 ALIGN=MIDDLE  ALT=\"%28t%5E2-0.5t-7.5%29%2Ft%28t-0.5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First consider the zeros of the denominator -- 0 and 0.5.  We need to remember these values and exclude them if they come up in the process of finding the zeros of the numerator.  For now, just realize that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb=0 ALIGN=MIDDLE  ALT=\"a%2Fb=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0 ALIGN=MIDDLE  ALT=\"a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%3C%3E0 ALIGN=MIDDLE  ALT=\"b%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Therefore, all we need to do is solve:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t%5E2-0.5t-7.5%29=0 ALIGN=MIDDLE  ALT=\"%28t%5E2-0.5t-7.5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply by 2 to get rid of those pesky decimal fraction coefficients\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2-t-15=0 ALIGN=MIDDLE  ALT=\"2t%5E2-t-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Conveniently, this factors:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-2.5 ALIGN=MIDDLE  ALT=\"t=-2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Neither of these values are 0 or 0.5 which would have made the denominator in the original equation go to zero, but we can exclude the negative value.  As much as it would be nice to make the clock run backwards sometimes, negative time just doesn't make sense.  So, our time up the mountain is 3 hours.\r<BR>\n" );
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document.write( "The time down the mountain, is 1/2 hour less, or 2.5 hours.  Therefore the total trip was 3 + 2.5 = 5.5 hours.<BR>\n" );
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