document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356937>Question 356937</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Engine pulls train 140 miles, 2nd engine is 5 mph faster than first, takes over and pull the train 200 miles, total time required for 6 hrs. \r<BR>\n" );
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document.write( "find the average rate of each engine. \r<BR>\n" );
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document.write( "totally stuck on the setup of the problem..  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #254881 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=254881\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Engine pulls train 140 miles,<BR>\n" );
document.write( " 2nd engine is 5 mph faster than first, takes over and pull the train 200 miles,<BR>\n" );
document.write( " total time required for 6 hrs.<BR>\n" );
document.write( "find the average rate of each engine.<BR>\n" );
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document.write( "Let s = speed of the slower engine<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+5) = speed of the faster<BR>\n" );
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document.write( "Write a time equation, Time = dist/speed<BR>\n" );
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document.write( "Slow engine time + fast engine time = 6 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140%2Fs ALIGN=MIDDLE  ALT=\"140%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2F%28%28s%2B5%29%29 ALIGN=MIDDLE  ALT=\"200%2F%28%28s%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6<BR>\n" );
document.write( "multiply by s(s+5), results<BR>\n" );
document.write( "140(s+5) + 200s = 6s(s+5)<BR>\n" );
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document.write( "140s + 700 + 200s = 6s^2 + 30s<BR>\n" );
document.write( "Arrange as a quadratic on the right<BR>\n" );
document.write( "0 = 6s^2 + 30s - 140s - 200s - 700<BR>\n" );
document.write( "6s^2 - 310s - 700 = 0<BR>\n" );
document.write( "Simplify, divide by 2<BR>\n" );
document.write( "3s^2 - 155s - 350 = 0<BR>\n" );
document.write( "Use the quadratic formula to find the positive solution<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-155%29+%2B-+sqrt%28-155%5E2-4%2A3%2A-350+%29%29%2F%282%2A3%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-155%29+%2B-+sqrt%28-155%5E2-4%2A3%2A-350+%29%29%2F%282%2A3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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