document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199563>Question 199563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3.	Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle. \r<BR>\n" );
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document.write( "i think it is 30mph but I cannot figure out the equation </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149972 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=149972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember, the distance-rate-time formula is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since he \"traveled 150 miles at a certain speed\", this means that the first equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150=rt ALIGN=MIDDLE  ALT=\"150=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > (simply plug in d=150)\r<BR>\n" );
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document.write( "The statement \"Had gone 20mph faster, the trip would have taken 2 hour less\", tells us that the next equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150=%28r%2B20%29%28t-2%29 ALIGN=MIDDLE  ALT=\"150=%28r%2B20%29%28t-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the distance is the same, but the speed is now 20 mph faster and the time is 2 hours shorter)\r<BR>\n" );
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document.write( "The goal is to use this system to solve for \"r\" (and if we want, \"t\" also)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150=rt ALIGN=MIDDLE  ALT=\"150=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2Fr=t ALIGN=MIDDLE  ALT=\"150%2Fr=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by r.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=150%2Fr ALIGN=MIDDLE  ALT=\"t=150%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150=%28r%2B20%29%28t-2%29 ALIGN=MIDDLE  ALT=\"150=%28r%2B20%29%28t-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move onto the second equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150=%28r%2B20%29%28150%2Fr-2%29 ALIGN=MIDDLE  ALT=\"150=%28r%2B20%29%28150%2Fr-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=150%2Fr ALIGN=MIDDLE  ALT=\"t=150%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150=150-2r%2B3000%2Fr-40 ALIGN=MIDDLE  ALT=\"150=150-2r%2B3000%2Fr-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150r=150r-2r%5E2%2B3000-40r ALIGN=MIDDLE  ALT=\"150r=150r-2r%5E2%2B3000-40r\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear out the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=150r-2r%5E2%2B3000-40r-150r ALIGN=MIDDLE  ALT=\"0=150r-2r%5E2%2B3000-40r-150r\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600r ALIGN=MIDDLE  ALT=\"600r\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-2r%5E2-40r%2B3000 ALIGN=MIDDLE  ALT=\"0=-2r%5E2-40r%2B3000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine and rearrange the terms.\r<BR>\n" );
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document.write( "Notice we have a quadratic in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ar%5E2%2BBr%2BC ALIGN=MIDDLE  ALT=\"Ar%5E2%2BBr%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-2 ALIGN=MIDDLE  ALT=\"A=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-40 ALIGN=MIDDLE  ALT=\"B=-40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=3000 ALIGN=MIDDLE  ALT=\"C=3000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for \"r\":\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"r+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28-%28-40%29+%2B-+sqrt%28+%28-40%29%5E2-4%28-2%29%283000%29+%29%29%2F%282%28-2%29%29 ALIGN=MIDDLE  ALT=\"r+=+%28-%28-40%29+%2B-+sqrt%28+%28-40%29%5E2-4%28-2%29%283000%29+%29%29%2F%282%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-2 ALIGN=MIDDLE  ALT=\"A=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-40 ALIGN=MIDDLE  ALT=\"B=-40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=3000 ALIGN=MIDDLE  ALT=\"C=3000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2840+%2B-+sqrt%28+%28-40%29%5E2-4%28-2%29%283000%29+%29%29%2F%282%28-2%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2840+%2B-+sqrt%28+%28-40%29%5E2-4%28-2%29%283000%29+%29%29%2F%282%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-40 ALIGN=MIDDLE  ALT=\"-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40 ALIGN=MIDDLE  ALT=\"40\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2840+%2B-+sqrt%28+1600-4%28-2%29%283000%29+%29%29%2F%282%28-2%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2840+%2B-+sqrt%28+1600-4%28-2%29%283000%29+%29%29%2F%282%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-40 ALIGN=MIDDLE  ALT=\"-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1600 ALIGN=MIDDLE  ALT=\"1600\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2840+%2B-+sqrt%28+1600--24000+%29%29%2F%282%28-2%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2840+%2B-+sqrt%28+1600--24000+%29%29%2F%282%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-2%29%283000%29 ALIGN=MIDDLE  ALT=\"4%28-2%29%283000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-24000 ALIGN=MIDDLE  ALT=\"-24000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2840+%2B-+sqrt%28+1600%2B24000+%29%29%2F%282%28-2%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2840+%2B-+sqrt%28+1600%2B24000+%29%29%2F%282%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281600--24000%29 ALIGN=MIDDLE  ALT=\"sqrt%281600--24000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281600%2B24000%29 ALIGN=MIDDLE  ALT=\"sqrt%281600%2B24000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2840+%2B-+sqrt%28+25600+%29%29%2F%282%28-2%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2840+%2B-+sqrt%28+25600+%29%29%2F%282%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1600 ALIGN=MIDDLE  ALT=\"1600\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24000 ALIGN=MIDDLE  ALT=\"24000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25600 ALIGN=MIDDLE  ALT=\"25600\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2840+%2B-+sqrt%28+25600+%29%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"r+=+%2840+%2B-+sqrt%28+25600+%29%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2840+%2B-+160%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"r+=+%2840+%2B-+160%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25600 ALIGN=MIDDLE  ALT=\"25600\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=160 ALIGN=MIDDLE  ALT=\"160\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2840+%2B+160%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"r+=+%2840+%2B+160%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2840+-+160%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"r+=+%2840+-+160%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28200%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"r+=+%28200%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=++%28-120%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"r+=++%28-120%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-50 ALIGN=MIDDLE  ALT=\"r+=+-50\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+30 ALIGN=MIDDLE  ALT=\"r+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the <i>possible</i> solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-50 ALIGN=MIDDLE  ALT=\"r+=+-50\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+30 ALIGN=MIDDLE  ALT=\"r+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Since a negative speed doesn't make any sense, this means that we must ignore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-50 ALIGN=MIDDLE  ALT=\"r+=+-50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+30 ALIGN=MIDDLE  ALT=\"r+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that he was traveling 30 mph. So you are correct, good job. </SPAN>\n" );
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