document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=534356>Question 534356</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a runner starts jogging at her house. She jogs 6 miles and then turns around and jogs back to her house. The first part of her job is mostly uphill, so her speed averages 3 miles per hour less than her returning spped. If the total time she spends jogging is 1 3/4 hours, find her speed going and her speed returning </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351490 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=351490\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a runner starts jogging at her house. She jogs 6 miles and then turns around and jogs back to her house. The first part of her job is mostly uphill, so her speed averages 3 miles per hour less than her returning speed. If the total time she spends jogging is 1 3/4 hours, find her speed going and her speed returning<BR>\n" );
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document.write( "let s = the uphill speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+3) = the downhill speed<BR>\n" );
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document.write( "Change time to 1.75 hrs<BR>\n" );
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document.write( "Write a time equation, time = dist/speed<BR>\n" );
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document.write( "Up time + down time = total time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fs ALIGN=MIDDLE  ALT=\"6%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%28%28s%2B3%29%29 ALIGN=MIDDLE  ALT=\"6%2F%28%28s%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.75<BR>\n" );
document.write( "multiply by s(s+3) to clear the denominators, results:<BR>\n" );
document.write( "6(s+3) + 6s = 1.75s(s+3)<BR>\n" );
document.write( "6s + 18 + 6s = 1.75s^2 + 5.25s<BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "0 = 1.75s + 5.25s - 12s - 18<BR>\n" );
document.write( "1.75s - 6.75s - 18 = 0<BR>\n" );
document.write( "Use the quadratic formula to find s<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = s; a=1.75, b=-6.75, c=-18<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-%286.67%29+%2B-+sqrt%28-6.75%5E2-4%2A1.75%2A-18+%29%29%2F%282%2A-1.75%29+ ALIGN=MIDDLE  ALT=\"s+=+%28-%286.67%29+%2B-+sqrt%28-6.75%5E2-4%2A1.75%2A-18+%29%29%2F%282%2A-1.75%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "You can do the rather tedious math here, you should get a positive solution<BR>\n" );
document.write( "s = 5.67 mph, the speed uphill, and obviously, 8.67 mph down </SPAN>\n" );
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