document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=512669>Question 512669</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On a 50 mile bike ride Irena averaged 4 mph faster for the first 36 miles than she did for the last 14 miles. The entire trop took 3 hours. Find her speed for the 36 miles </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #342809 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=342809\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> On a 50 mile bike ride Irena averaged 4 mph faster for the first 36 miles than she did for the last 14 miles.<BR>\n" );
document.write( " The entire trip took 3 hours. Find her speed for the 36 miles<BR>\n" );
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document.write( "let s = the speed for the 1st 36 mi<BR>\n" );
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document.write( "Write a time equation; time = dist/speed<BR>\n" );
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document.write( "36mi time + 14 mi time = 3 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2Fs ALIGN=MIDDLE  ALT=\"36%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F%28%28s-4%29%29 ALIGN=MIDDLE  ALT=\"14%2F%28%28s-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
document.write( "Multiply by s(s-4)<BR>\n" );
document.write( "s(s-4)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2Fs ALIGN=MIDDLE  ALT=\"36%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + s(s-4)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F%28%28s-4%29%29 ALIGN=MIDDLE  ALT=\"14%2F%28%28s-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = s(s-4)*3<BR>\n" );
document.write( "cancel the denominators<BR>\n" );
document.write( "36(s-4) + 14s = 3s(s-4)<BR>\n" );
document.write( "36s - 144 + 14s = 3x^2 - 12s<BR>\n" );
document.write( "50s - 144 = 3x^2 - 12s<BR>\n" );
document.write( "arrange as a quadratic equation on the right<BR>\n" );
document.write( "0 = 3s^2 - 12s - 50s + 144 <BR>\n" );
document.write( "3x^2 - 62s + 144 = 0<BR>\n" );
document.write( "you can use the quadratic formula, but this will factor to:<BR>\n" );
document.write( "(3s-8)(s-18) = 0<BR>\n" );
document.write( "The reasonable solution<BR>\n" );
document.write( "s = 18 mph for the 1st 36 mi<BR>\n" );
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document.write( "Check this by finding the time at each speed<BR>\n" );
document.write( "36/18 = 2 hrs<BR>\n" );
document.write( "14/14 = 1 hr<BR>\n" );
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