document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163342>Question 163342</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a car had increased its average speed for a 18-mile journey by 5 mph, the journey would have been completed in 30 minutes less.  What was the car's original average speed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120344 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=120344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a car had increased its average speed for a 18-mile journey by 5 mph, the journey would have been completed in 30 minutes less. What was the car's original average speed?<BR>\n" );
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document.write( "Just looking at this we have to assume the car's speed will be awfully slow!<BR>\n" );
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document.write( "Let s = car's original speed<BR>\n" );
document.write( "Then<BR>\n" );
document.write( "(s+5) = cars increased speed<BR>\n" );
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document.write( "The distances at both speeds is given as 18 mi<BR>\n" );
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document.write( "Change 30 min to .5 hrs<BR>\n" );
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document.write( "Write a time equation: Time = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=distance%2Fspeed ALIGN=MIDDLE  ALT=\"distance%2Fspeed\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Original speed time - half hour = increased speed time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Fs ALIGN=MIDDLE  ALT=\"18%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - .5 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F%28%28s%2B5%29%29 ALIGN=MIDDLE  ALT=\"18%2F%28%28s%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply equation by s(s+5):<BR>\n" );
document.write( "s(s+5)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Fs ALIGN=MIDDLE  ALT=\"18%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - s(s+5)*.5 = s(s+5)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F%28%28s%2B5%29%29 ALIGN=MIDDLE  ALT=\"18%2F%28%28s%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cancel the denominators and you have:<BR>\n" );
document.write( "18(s+5) - .5(s^2 + 5s) = 18s<BR>\n" );
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document.write( "Multiply what's in the brackets<BR>\n" );
document.write( "18s + 90 - .5s^2 - 2.5s = 18s<BR>\n" );
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document.write( "Arrange as a quadratic equation:<BR>\n" );
document.write( "-.5s^2 + 18s - 18s - 2.5s + 90 = 0<BR>\n" );
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document.write( "-.5s^2 - 2.5s + 90 = 0<BR>\n" );
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document.write( "Multiply equation by -2 to get rid of the decimals and change the signs;<BR>\n" );
document.write( "s^2 + 5s - 180<BR>\n" );
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document.write( "This will not factor, use the quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this problem a=1; b=5; c=-180<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-5+%2B-+sqrt%28+5%5E2-+4%2A1%2A-180+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"s+=+%28-5+%2B-+sqrt%28+5%5E2-+4%2A1%2A-180+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-5+%2B-+sqrt%2825+%2B+720+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"s+=+%28-5+%2B-+sqrt%2825+%2B+720+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-5+%2B-+sqrt%28745%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"s+=+%28-5+%2B-+sqrt%28745%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the positive solution here:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-5+%2B+27.29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"s+=+%28-5+%2B+27.29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22.29%2F2 ALIGN=MIDDLE  ALT=\"22.29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 11.15 mph is the original speed<BR>\n" );
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document.write( "Check solution by finding the times<BR>\n" );
document.write( "11.15 + 56 = 16.15 is the faster speed<BR>\n" );
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document.write( "18/11.15 = 1.6 hrs<BR>\n" );
document.write( "18/16.15 = 1.1 hrs<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "differ by .5 hrs as indicated<BR>\n" );
document.write( " </SPAN>\n" );
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