document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=408154>Question 408154</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a new schedule for a train requires it to go 270 miles in 26 minutes less time than before. To do thsi it must average 4 mpoh faster. What must its new average speed be? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287618 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=287618\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a new schedule for a train requires it to go 270 miles in 26 minutes less time than before.<BR>\n" );
document.write( " To do this it must average 4 mph faster.<BR>\n" );
document.write( " What must its new average speed be?<BR>\n" );
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document.write( "Let s = the new average speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-4) = the old average speed<BR>\n" );
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document.write( "Change 26 min to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26%2F60 ALIGN=MIDDLE  ALT=\"26%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F30 ALIGN=MIDDLE  ALT=\"13%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( ":<BR>\n" );
document.write( "write a time equation: time = dist/speed<BR>\n" );
document.write( "Old time - new time = 26 min<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270%2F%28s-4%29 ALIGN=MIDDLE  ALT=\"270%2F%28s-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270%2Fs ALIGN=MIDDLE  ALT=\"270%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F30 ALIGN=MIDDLE  ALT=\"13%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply equation by 30s(s-4) to get rid of the denominators, results:<BR>\n" );
document.write( "30s(270) - 30(s-4)(270) = 13s(s-4)<BR>\n" );
document.write( "8100s - 8100(s-4) = 13s^2 - 52s<BR>\n" );
document.write( "8100s - 8100s + 32400 = 13s^2 - 52s<BR>\n" );
document.write( "Combine to form a quadratic equation<BR>\n" );
document.write( "0 = 13s^2 - 52s - 32400 <BR>\n" );
document.write( "Solve this using the quadratic formula a=13, b=-52, c=-32400<BR>\n" );
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document.write( "The positive solution: s = 51.963 ~ 52 mph is the new average speed<BR>\n" );
document.write( ";<BR>\n" );
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document.write( "Check solution in decimals<BR>\n" );
document.write( "270/48 - 270/52 = .4327 * 60 ~ 26.0 min </SPAN>\n" );
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