document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=709710>Question 709710</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a 60km bicycle race, a rider calculates that if he can increase his speed by 6km/h he will cut his time for the distance by 20minutes. What was his original speed?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436765 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=436765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a 60km bicycle race, a rider calculates that if he can increase his speed by 6km/h he will cut his time for the distance by 20minutes. What was his original speed?<BR>\n" );
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document.write( "Change 20 min to 1/3 hr<BR>\n" );
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document.write( "Let s = original speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+6) = increased speed<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=60%2Fx ALIGN=MIDDLE  ALT=\"60%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F%28%28s%2B6%29%29 ALIGN=MIDDLE  ALT=\"60%2F%28%28s%2B6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply by 3s(s+6) to clear the denominators, resulting in:<BR>\n" );
document.write( "3(s+6)(60) + 3s(60) = s(s+6)<BR>\n" );
document.write( "180s + 1080 + 180s = s^2 + 6s<BR>\n" );
document.write( "A quadratic equation from all this<BR>\n" );
document.write( "s^2 + 6s - 1080 = 0 <BR>\n" );
document.write( "You can solve this using the quadratic formula if you enjoy that sort of thing. But this will factor to:<BR>\n" );
document.write( "(s + 36)(s + 30) = 0<BR>\n" );
document.write( "The positive solution is all we want here<BR>\n" );
document.write( "s = 30 km/hr is the original speed<BR>\n" );
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document.write( "Check this by finding the actual times<BR>\n" );
document.write( "60/30 = 2 hrs<BR>\n" );
document.write( "60/36 = 1.67<BR>\n" );
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document.write( "differ: .33 hrs which is 20 min </SPAN>\n" );
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