document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135051>Question 1135051</A>: <I><SPAN STYLE=\"word-break: break-all;\"> julie recently drove to visit her parents who live 240 miles away. on her way there her average speed was 11 miles per hour faster than on her way home (she ran into some bad weather). if julie spent a total of 8 hours driving, find the two rates<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752586 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=752586\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = distance.\r<BR>\n" );
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document.write( "on her way there, she drove 11 miles per hour faster than on her way home.\r<BR>\n" );
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document.write( "the total time spent driving was 8 hours.\r<BR>\n" );
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document.write( "let x = her rate of speed going.\r<BR>\n" );
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document.write( "let y = the time it took her to get there.\r<BR>\n" );
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document.write( "the formula for going to her parents home is x * y = 240\r<BR>\n" );
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document.write( "since she traveled 11 miles per hour faster going, then her rate of speed coming back has to be x - 11 because x miles per hour is 11 miles per hour faster than x - 11 miles per hour.\r<BR>\n" );
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document.write( "coming back her time was 8 - y.\r<BR>\n" );
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document.write( "the formula for coming back from her parent's home is (x - 11) * (8 - y) = 240\r<BR>\n" );
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document.write( "you have two equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "x * y = 240 and (x - 11) * (8 - y) = 240\r<BR>\n" );
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document.write( "since they are both equal to 240, you can set x * y equal to (x - 11) * (8 - y) to get:\r<BR>\n" );
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document.write( "x * y = (x - 11) * (8 - y)\r<BR>\n" );
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document.write( "multiply the factors in the right side of this equation to get:\r<BR>\n" );
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document.write( "xy = 8x - xy - 88 + 11y\r<BR>\n" );
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document.write( "in the first equation of xy = 240, solve for y to get y = 240 / x\r<BR>\n" );
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document.write( "replace y with 240 / x in the second equation to get:\r<BR>\n" );
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document.write( "x * 240/x = 8x - x * 240/x - 88 + 11 * 240 / x\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "240 = 8x - 240 - 88 + 2640 / x\r<BR>\n" );
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document.write( "multiply both sides of this equation by x to get\r<BR>\n" );
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document.write( "240x = 8x^2 - 240x - 88x + 2640\r<BR>\n" );
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document.write( "subtract 240x from both sides of this equation to get:\r<BR>\n" );
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document.write( "0 = 8x^2 - 240x - 88x + 2640 - 240x\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "0 = 8x^2 - 568x + 2640\r<BR>\n" );
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document.write( "divide both sides of this equation by 8 to get:\r<BR>\n" );
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document.write( "0 = x^2 - 71x + 330\r<BR>\n" );
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document.write( "factor this quadratic equation to get:\r<BR>\n" );
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document.write( "x = 5 or x = 66\r<BR>\n" );
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document.write( "in the first equation of x * y = 240, replace x with 5 and solve for y to get y = 240 / 5 = 48\r<BR>\n" );
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document.write( "still in the first equation of x * y = 240, replace x with 66 and solve for y to get y = 3.636\r<BR>\n" );
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document.write( "since the total time is 8 hours, y can't be 48, so y must be equal to 3.636363636 hours which forces x to be equal to 66.\r<BR>\n" );
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document.write( "x is the speed, so x is 66 miles per hour and it took 3.636363636 hours to get to her parent's house.\r<BR>\n" );
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document.write( "coming back she traveled 66 - 11 miles per hour and took 8 - 3.636363636 hours.\r<BR>\n" );
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document.write( "that means she traveled 55 miles per hour for 4.363636364 hours.\r<BR>\n" );
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document.write( "55 miles per hour for 4.363636364 hours equals 240 miles.\r<BR>\n" );
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document.write( "the solution looks good.\r<BR>\n" );
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document.write( "looks messy but it's right as far as i can tell.\r<BR>\n" );
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document.write( "your solution is that she traveled at 66 miles per hour to get to her parent's home and she traveled at 55 miles per hour coming back.\r<BR>\n" );
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