document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=231453>Question 231453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Amy drove the 200 miles to New Orleans at an average speed 10 miles per hour faster than her usual average speed. If she completed the trip in 1 hour less than usual, what is her usual driving speed in miles per hour.\r<BR>\n" );
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document.write( "I know the answer is 40 miles per hour, but how did they come up with this? I think there is numbers missing in this problem.<BR>\n" );
document.write( "Thank you,<BR>\n" );
document.write( "Katie </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171296 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=171296\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> distance = 200 miles<BR>\n" );
document.write( "Her usual speed is X miles per hour since we don't know it.<BR>\n" );
document.write( "Her usual time is T hours because we don't know that either.\r<BR>\n" );
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document.write( "Problem states that she traveled 10 miles per hour faster than her usual speed.\r<BR>\n" );
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document.write( "This makes the speed she traveled at equal to X + 10.\r<BR>\n" );
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document.write( "Problem states that she took 1 hour less.\r<BR>\n" );
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document.write( "This makes the time she took equal to T - 1.\r<BR>\n" );
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document.write( "She normally travels at X miles per hours and takes T hours.\r<BR>\n" );
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document.write( "Since rate * time = distance, we get:\r<BR>\n" );
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document.write( "X * T = 200\r<BR>\n" );
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document.write( "This time she traveled 10 miles per hour faster and took 1 hour less.\r<BR>\n" );
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document.write( "This time, we get:\r<BR>\n" );
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document.write( "(X+10) * (T-1) = 200\r<BR>\n" );
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document.write( "Since they are both equal to 200, then they are both equal to each other, so we get:\r<BR>\n" );
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document.write( "X*T = (X+10)*(T-1)\r<BR>\n" );
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document.write( "We simplify this by multiplying out all terms to get:\r<BR>\n" );
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document.write( "X*T = X*T - X + 10T - 10\r<BR>\n" );
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document.write( "We have one equation in two unknowns, but we can substitute for one of the unknowns and solve for the other.\r<BR>\n" );
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document.write( "We'll take the equation X*T = 200 and solve for T to get T = 200/X\r<BR>\n" );
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document.write( "We'll then replace T in our equation of X*T = X*T - X + 10T - 10 to get:\r<BR>\n" );
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document.write( "X*200/X = X*200/X - X + 10*200/X - 10.\r<BR>\n" );
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document.write( "We'll simplify this equation to get:\r<BR>\n" );
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document.write( "200 = 200 - X + 2000/X - 10.\r<BR>\n" );
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document.write( "We'll subtract 200 and we'll add X and we'll subtract 2000/X and we'll add 10 to both sides of this equation to get:\r<BR>\n" );
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document.write( "X - 2000/X + 10 = 0\r<BR>\n" );
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document.write( "We'll multiply both sides of this equation by X to get:\r<BR>\n" );
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document.write( "X^2 + 10X - 2000 = 0\r<BR>\n" );
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document.write( "This factors out to:\r<BR>\n" );
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document.write( "(X-40) * (X+50) = 0\r<BR>\n" );
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document.write( "X can be either 40 or -50.\r<BR>\n" );
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document.write( "since X can't be negative, we are left with X = 40.\r<BR>\n" );
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document.write( "Since X*T = 200, We get T = 5\r<BR>\n" );
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document.write( "Our answer is:\r<BR>\n" );
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document.write( "X = 40<BR>\n" );
document.write( "T = 5\r<BR>\n" );
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document.write( "40*5 = 200 which is the normal time at the normal rate.\r<BR>\n" );
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document.write( "50*4 = 200 which is 1 hour less than the normal time at 10 miles per hour more than the normal rate.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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