document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167469>Question 167469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help!<BR>\n" );
document.write( "At the Indianapolis 500, Carter and Daniels were participants. Daniels'motor blew after 240 miles, and Carter was out after 270 miles. If Carter's average rate was 20mph more than Daniels, and their total time was 3 hours, how fast was each averaging?\r<BR>\n" );
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document.write( "Thank you for your help, whichever kind person answers my question!\r<BR>\n" );
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document.write( "Lauren </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123404 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=123404\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At the Indianapolis 500, Carter and Daniels were participants. Daniel's motor<BR>\n" );
document.write( " blew after 240 miles, and Carter was out after 270 miles. If Carter's average<BR>\n" );
document.write( " rate was 20mph more than Daniels, and their total time was 3 hours,<BR>\n" );
document.write( " how fast was each averaging?<BR>\n" );
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document.write( "Let s = D's speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+20) = C's speed<BR>\n" );
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document.write( "Write a time equation: Time = dist/speed<BR>\n" );
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document.write( "D's time + C's time = 5 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240%2Fs ALIGN=MIDDLE  ALT=\"240%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270%2F%28%28s%2B20%29%29 ALIGN=MIDDLE  ALT=\"270%2F%28%28s%2B20%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
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document.write( "Multiply equation by s(s+20)<BR>\n" );
document.write( "s(s+20)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240%2Fs ALIGN=MIDDLE  ALT=\"240%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + s(s+20)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270%2F%28%28s%2B20%29%29 ALIGN=MIDDLE  ALT=\"270%2F%28%28s%2B20%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = s(s+20)*3<BR>\n" );
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document.write( "Cancel out the denominators and you have:<BR>\n" );
document.write( "240(s+20) + 270s = 3s(s+20)<BR>\n" );
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document.write( "240s + 4800 + 270s = 3s^2 + 60s<BR>\n" );
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document.write( "510s + 4800 = 3s^2 + 60s<BR>\n" );
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document.write( "0 = 3s^2 + 60s - 510s - 4800<BR>\n" );
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document.write( "A quadratic equation<BR>\n" );
document.write( "3s^2 - 450s - 4800 = 0<BR>\n" );
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document.write( "Simplify divide by 3<BR>\n" );
document.write( "s^2 - 150s - 1600 = 0<BR>\n" );
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document.write( "Factors to:<BR>\n" );
document.write( "(s - 160)(x + 10) = 0<BR>\n" );
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document.write( "Positive solution is what we want here:<BR>\n" );
document.write( "s = +160 mph is D's speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "160 + 20 = 180 mph is C's speed.<BR>\n" );
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document.write( "Check solution in original time equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240%2F160 ALIGN=MIDDLE  ALT=\"240%2F160\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270%2F180 ALIGN=MIDDLE  ALT=\"270%2F180\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( "1.5 + 1.5 = 3 hrs; confirms our solution<BR>\n" );
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document.write( "by a kind person! </SPAN>\n" );
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