document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=466759>Question 466759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A relay race required runners to run from Point A to Point B and then back to point A. the distance from A to B = 22km.\r<BR>\n" );
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document.write( "On the return trip (Point B to Point A) the runners average speed decreased by (1.2km/hr). \r<BR>\n" );
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document.write( "If the relay took 10.5 hours to complete, what was the average speed from Point A to Point B.<BR>\n" );
document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #320051 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=320051\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A relay race required runners to run from Point A to Point B and then back to point A. the distance from A to B = 22km.\r<BR>\n" );
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document.write( "On the return trip (Point B to Point A) the runners average speed decreased by (1.2km/hr). \r<BR>\n" );
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document.write( "If the relay took 10.5 hours to complete, what was the average speed from Point A to Point B.<BR>\n" );
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document.write( "Let s = av speed from Point A to B<BR>\n" );
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document.write( "It says,\"On the return trip (Point B to Point A) the runners average speed decreased by (1.2km/hr).\" therefore:<BR>\n" );
document.write( "(s-1.2) = return trip speed (B to A)<BR>\n" );
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document.write( "Write a time equation; time = dist/speed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%2Fs ALIGN=MIDDLE  ALT=\"22%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%2F%28%28s-1.2%29%29 ALIGN=MIDDLE  ALT=\"22%2F%28%28s-1.2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10.5<BR>\n" );
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document.write( "Multiply by s(s-1.2), results:<BR>\n" );
document.write( "22(s-1.2) + 22s = 10.5s(s-1.2)<BR>\n" );
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document.write( "22s - 26.4 + 22s = 10.5s^2 - 12.6s<BR>\n" );
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document.write( "44s - 26.4 = 10.5s^2 - 12.6s<BR>\n" );
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document.write( "0 = 10.5s^2 - 12.6s - 44s + 26.4<BR>\n" );
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document.write( "A quadratic equation<BR>\n" );
document.write( "10.5s^2 - 56.6s + 26.4 = 0<BR>\n" );
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document.write( "Multiply by 10 to get rid of the decimals<BR>\n" );
document.write( "105s^2 - 566s + 264 = 0<BR>\n" );
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document.write( "Use the quadratic formula to solve this<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( "a=105, b=-566, c=264, s=x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-%28-566%29+%2B-+sqrt%28-566%5E2-4%2A105%2A264+%29%29%2F%282%2A105%29+ ALIGN=MIDDLE  ALT=\"s+=+%28-%28-566%29+%2B-+sqrt%28-566%5E2-4%2A105%2A264+%29%29%2F%282%2A105%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28566+%2B-+sqrt%28320356-110880+%29%29%2F%28210%29+ ALIGN=MIDDLE  ALT=\"s+=+%28566+%2B-+sqrt%28320356-110880+%29%29%2F%28210%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28566+%2B-+sqrt%28209476%29%29%2F%28210%29+ ALIGN=MIDDLE  ALT=\"s+=+%28566+%2B-+sqrt%28209476%29%29%2F%28210%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions, but only this one will make sense<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28566+%2B+457.7%29%2F%28210%29+ ALIGN=MIDDLE  ALT=\"s+=+%28566+%2B+457.7%29%2F%28210%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1023.7%2F210 ALIGN=MIDDLE  ALT=\"1023.7%2F210\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 4.87 km/hr, av speed from A to B<BR>\n" );
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document.write( "Check this by finding the times<BR>\n" );
document.write( "22/4.87 = 4.5 hrs<BR>\n" );
document.write( "22/3.67 = 6.0 hrs<BR>\n" );
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document.write( "tot time: 10.5 hrs, confirms our solution </SPAN>\n" );
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