document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=521731>Question 521731</A>: <I><SPAN STYLE=\"word-break: break-all;\"> amy drove 200 miles at an average speed 10 miles per hour faster than her usual speed. if she completed the trip in 1 hour less time than usual, what is her usual driving speed in miles per hour? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #346572 by </B><A HREF=/tutors/aboutme.mpl?userid=mamiya><B>mamiya(56)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mamiya><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=346572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x be the usual average speed and t the among of times she usually  took to complete the trip.  let s be the average speed , t' the among of time she takes now and d the distance.\r<BR>\n" );
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document.write( " s= x + 10    since her average speed now is 10 miles per hour more than her usual speed<BR>\n" );
document.write( " d= 200 miles  <BR>\n" );
document.write( " t'= t - 1   since she completed the trip in 1 hour less time usual\r<BR>\n" );
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document.write( "we know that distance= speed x time <BR>\n" );
document.write( "so d= st'   and    d= xt\r<BR>\n" );
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document.write( "so      xt= 200<BR>\n" );
document.write( "       (x+10)(t-1)=200\r<BR>\n" );
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document.write( "      xt=200<BR>\n" );
document.write( "     xt - x + 10t -10= 200\r<BR>\n" );
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document.write( "   xt=200<BR>\n" );
document.write( "  200 - x + 10t - 10 =200\r<BR>\n" );
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document.write( "  xt=200<BR>\n" );
document.write( "  10t - x= 10<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  x= 10(t - 1)<BR>\n" );
document.write( "  xt=200\r<BR>\n" );
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document.write( "  x= 10(t-1)<BR>\n" );
document.write( "  10(t-1)*t = 200\r<BR>\n" );
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document.write( "  10t^2 - 10t - 200 =0<BR>\n" );
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document.write( "  t^2 - t - 20 =0\r<BR>\n" );
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document.write( "let's call p(x)= t^2 - t - 20 and let's factorize this polynomial.<BR>\n" );
document.write( "the determinant D= (-1)^2 - 4(1)(-20)= 81= (9)^2  <BR>\n" );
document.write( "  t1= (1+9)/2 = 5<BR>\n" );
document.write( "  t2= (1-9)/2 = -4<BR>\n" );
document.write( "so the answers of the equation ( t^2-T-20=0) are 5 and -4, but since t is an among of time , t has to be a positive number, so answer can't be -4 , therefore the answer is 5. \r<BR>\n" );
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document.write( "so t=5<BR>\n" );
document.write( "x=10(t-1)<BR>\n" );
document.write( " = 10(5-1)<BR>\n" );
document.write( " = 40 \r<BR>\n" );
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document.write( "so, her usual driving speed is 40 miles per hour.\r<BR>\n" );
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document.write( "   \r<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );