document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80688>Question 80688</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57851 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=57851\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "distance(d) equals rate(r) times time(t) or d=rt; t=d/r and r=d/t\r<BR>\n" );
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document.write( "let r=initial speed\r<BR>\n" );
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document.write( "travel time at initial speed =200/r\r<BR>\n" );
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document.write( "travel time at 10 mph faster=200/(r+10)\r<BR>\n" );
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document.write( "Now we are told that the travel time at 10 mph faster (200/(r+10)) is 1 hour less than the travel time at the initial speed (200/r).  So our equation to solve is:\r<BR>\n" );
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document.write( "(200/r)-1=200/(r+10)  multiply both sides by r(r+10) to get rid of fractions\r<BR>\n" );
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document.write( "200(r+10)-r(r+10)=200r  get rid of parens\r<BR>\n" );
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document.write( "200r+2000-r^2-10r=200r subtract 200r from both sides\r<BR>\n" );
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document.write( "200r-200r+2000-r^2-10r=200r-200r  collect like terms\r<BR>\n" );
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document.write( "2000-r^2-10r=0  multiply each term by -1\r<BR>\n" );
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document.write( "r^2+10r-2000=0  quadratic in standard form and it can be factored.<BR>\n" );
document.write( "(Note: If the A coefficient of a quadratic is 1, then the B coefficient will be the sum of the factors of the C coefficient.  In this case, the factors of -2000 that add up to +10 are +50 and -40)\r<BR>\n" );
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document.write( "(r+50)(r-40)=0<BR>\n" );
document.write( "r=-50 mph-------------------------discount negative speed\r<BR>\n" );
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document.write( "and<BR>\n" );
document.write( "r=40 mph-------------------------------initial speed\r<BR>\n" );
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document.write( "Check\r<BR>\n" );
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document.write( "200/40=5 hr<BR>\n" );
document.write( "200/50=4 hr<BR>\n" );
document.write( "5 hr - 4 hr =1 hr\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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