document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=296406>Question 296406</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jo runs up a mountain trail 4 miles long and then returns on the same trail downhill. Uphill she goes one mile per hour faster than half her downhill rate. If the round trip is one hour and forty minutes, then what is her downhill rate? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #213616 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=213616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Joe runs up a mountain trail 4 miles long and then returns on the same trail downhill.<BR>\n" );
document.write( " Uphill he goes one mile per hour faster than half his downhill rate.<BR>\n" );
document.write( " If the round trip is one hour and forty minutes, then what is his downhill rate?<BR>\n" );
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document.write( "Change 1 hr 40 min to: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F3 ALIGN=MIDDLE  ALT=\"5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
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document.write( "Let r = his downhill rate<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(.5r+1) = his uphill rated<BR>\n" );
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document.write( "Write a time equation: Time = distance/rate<BR>\n" );
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document.write( "Time up + time down = 1<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28%28.5r%2B1%29%29 ALIGN=MIDDLE  ALT=\"4%2F%28%28.5r%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fr ALIGN=MIDDLE  ALT=\"4%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F3 ALIGN=MIDDLE  ALT=\"5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply equation by 3r(.5r+1), results<BR>\n" );
document.write( "4(3r) + 4*3(.5r+1) = 5r(.5r+1)<BR>\n" );
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document.write( "12r + 12(.5r+1) = 2.5r^2 + 5r<BR>\n" );
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document.write( "12r + 6r + 12 = 2.5r^2 + 5r<BR>\n" );
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document.write( "18r + 12 = 2.5r^2 + 5r<BR>\n" );
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document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( "0 = 2.5r^2 + 5r - 18r - 12 <BR>\n" );
document.write( "2.5r^2 - 13r - 12 = 0<BR>\n" );
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document.write( "multiply by 2 to get rid of the decimal<BR>\n" );
document.write( "5r^2 - 26r - 24 = 0<BR>\n" );
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document.write( "Factors to<BR>\n" );
document.write( "(5r + 4)(r - 6) = 0<BR>\n" );
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document.write( "Positive solution<BR>\n" );
document.write( "r = 6 mph is the downhill rate<BR>\n" );
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document.write( "Check the solution: .5(6) + 1 = 4 mph is the uphill rate<BR>\n" );
document.write( "Times<BR>\n" );
document.write( "4/4 + 4/6 = 10/6 = 5/3 hr </SPAN>\n" );
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