document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=556604>Question 556604</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Deni walks to work and back on the same path. She walks on level ground at 4 MPH, uphill at 3 1/3 MPH, and downhill at 5 MPH. To get to work, she walks first on level ground and then up a hill. If her total time for the round trip is 2 1/2 hours, how many miles does she travel to work?\r<BR>\n" );
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document.write( "This problem has been stressing me out because i know that i have to set something = 2 1/2 hours but i have only delt with two other speeds, not 6 or 3 depending on how you look at it.\r<BR>\n" );
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document.write( "Thank you for the help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #362212 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=362212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Deni walks to work and back on the same path.<BR>\n" );
document.write( " She walks on level ground at 4 MPH, uphill at 3 1/3 MPH, and downhill at 5 MPH.<BR>\n" );
document.write( " To get to work, she walks first on level ground and then up a hill.<BR>\n" );
document.write( " If her total time for the round trip is 2 1/2 hours, how many miles does she travel to work?<BR>\n" );
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document.write( "Let x = level ground dist<BR>\n" );
document.write( "Let y = hill distance<BR>\n" );
document.write( ":\r<BR>\n" );
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document.write( "We can write a time equation for the round trip: time = dist/speed:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F3.33 ALIGN=MIDDLE  ALT=\"y%2F3.33\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F5 ALIGN=MIDDLE  ALT=\"y%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%2F4 ALIGN=MIDDLE  ALT=\"%282x%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F3.33 ALIGN=MIDDLE  ALT=\"y%2F3.33\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F5 ALIGN=MIDDLE  ALT=\"y%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.5<BR>\n" );
document.write( "multiply thru by 4*3.33*5 = 66.66 to clear the denominators, cancel we have:<BR>\n" );
document.write( "16.665(2x) + 20y + 13.333y = 66.66(2.5)<BR>\n" );
document.write( "33.333x + 20y + 13.333y = 166.66<BR>\n" );
document.write( "33.333x + 33.333y = 166.66<BR>\n" );
document.write( "33.333y = -33.333x + 166.66<BR>\n" );
document.write( "divide thru by 33.333 and we have a simple equaiton<BR>\n" );
document.write( "y = -x + 5<BR>\n" );
document.write( "From this equation we can find an x,y combination that will make sense<BR>\n" );
document.write( "there are more than one set of solutions to this<BR>\n" );
document.write( "Let x = 2 mi on the level<BR>\n" );
document.write( "y = -2 + 5<BR>\n" );
document.write( "then<BR>\n" );
document.write( "y = 3 mi on the hill<BR>\n" );
document.write( "therefore:<BR>\n" );
document.write( "2 + 3 + 3 + 2 = 10 miles to work<BR>\n" );
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document.write( "see if this checks out time-wise<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F4 ALIGN=MIDDLE  ALT=\"2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F3.33%29%29%29+%2B+%7B%7B%7B3%2F5 ALIGN=MIDDLE  ALT=\"3%2F3.33%29%29%29+%2B+%7B%7B%7B3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F4 ALIGN=MIDDLE  ALT=\"2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( ".5 + .9 + .6 + .5 = 2.5 hrs<BR>\n" );
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document.write( "It's interesting that any of the positive solutions will add up 10 miles which is what they want </SPAN>\n" );
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