document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255014>Question 255014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On the 42 km go kart course Arshia drives .4 km/hr faster than Sarah, but she has engine trouble part way around the track and has to stop to get the cart fixed.  This stop costs Arshia one half hour, and so she arrives 15 minutes after Sarah at the end of the course. How fast did each girl drive and how long did each girl take to finish the course?  I think that Sarah drove 52.5 km/hour and finished the course in 48 minutes.  I then think that Arshia drove 52.9 km/h and took 63 mins to complete the course.  I really am hoping that this correct and could certainly use some help if not.  Thanks so much for your time.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187319 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=187319\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> On the 42 km go kart course Arshia drives .4 km/hr faster than Sarah, but she has engine trouble part way around the track and has to stop to get the cart fixed.<BR>\n" );
document.write( " This stop costs Arshia one half hour, and so she arrives 15 minutes after Sarah at the end of the course.<BR>\n" );
document.write( " How fast did each girl drive and how long did each girl take to finish the course? <BR>\n" );
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document.write( "I am not sure how you did this, but here's my take on it:<BR>\n" );
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document.write( "Change 15 min to .25 hr<BR>\n" );
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document.write( "Let s = Sarah's speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+.4) = Arshia's speed<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42%2Fs ALIGN=MIDDLE  ALT=\"42%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = S's travel time<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42%2F%28%28s%2B.4%29%29%7D%7D+%2B+.5+=+A%27s+travel+time%0D%0A%3A%0D%0AS%27s+travel+time+%2B+15+min+=+A%27s+travel+time+%2B+half+hr%0D%0A%7B%7B%7B42%2Fs ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > + .25 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42%2F%28%28s%2B.4%29%29 ALIGN=MIDDLE  ALT=\"42%2F%28%28s%2B.4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5 <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42%2Fs ALIGN=MIDDLE  ALT=\"42%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42%2F%28%28s%2B.4%29%29 ALIGN=MIDDLE  ALT=\"42%2F%28%28s%2B.4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5 - .25<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42%2Fs ALIGN=MIDDLE  ALT=\"42%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42%2F%28%28s%2B.4%29%29 ALIGN=MIDDLE  ALT=\"42%2F%28%28s%2B.4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .25<BR>\n" );
document.write( "Multiply by s(s+.4), results<BR>\n" );
document.write( "42(s+.4) = 42s + .25s(s+.4)<BR>\n" );
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document.write( "42s + 16.8 = 42s + .25s^2 + .1s<BR>\n" );
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document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( ".25s^2 + .1s + 42s - 42s - 16.8 = 0<BR>\n" );
document.write( ".25s^2 + .1s - 16.8 = 0<BR>\n" );
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document.write( "Multiply by 20, get rid of those decimals<BR>\n" );
document.write( "5s^2 + 2s - 336 = 0<BR>\n" );
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document.write( "Factor this to<BR>\n" );
document.write( "(5s + 42)(s-8) = 0<BR>\n" );
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document.write( "positive solution<BR>\n" );
document.write( "s = 8 km/h is Sarah's speed<BR>\n" );
document.write( "and<BR>\n" );
document.write( "8.4 km/h is Arshia's speed<BR>\n" );
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document.write( "Find the times of each:<BR>\n" );
document.write( "42/8 = 5.25 hrs <BR>\n" );
document.write( "42/8.4 = 5 hrs, + .5  = 5.5 hrs (checks out, 15 min after Sarah) <BR>\n" );
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