document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058835>Question 1058835</A>: <I><SPAN STYLE=\"word-break: break-all;\"> you drive 28 miles to a friend's house and it takes you 1.26 hours to get there. Suppose that your speed during the second 14 miles was 5 MPH faster than your speed during the first 14 miles. What was your speed during the first 14 miles? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673937 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=673937\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the answer will be that you drove at 20 miles per hour for 14 miles and you drove at 25 miles per hour for 14 miles.<BR>\n" );
document.write( "your speed during the first 14 miles was 20 miles per hour.<BR>\n" );
document.write( "that would be your solution.<BR>\n" );
document.write( "here's how i derived that.\r<BR>\n" );
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document.write( "you are given that the total time took 1.26 hours.<BR>\n" );
document.write( "if you let x = the time for the first 14 miles, the 1.26 - x equals the time for the second 14 miles.\r<BR>\n" );
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document.write( "if you let y equal the rate you traveled at for the first 14 miles, then y + 5 equals the rate you traveled at for the second 14 miles.\r<BR>\n" );
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document.write( "since rate * time = distance, your formulas become:\r<BR>\n" );
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document.write( "x * y = 14 for the first 14 miles.<BR>\n" );
document.write( "(1.26 - x) * (y + 5) = 14 for the second 4 miles.\r<BR>\n" );
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document.write( "solve for y in the first formula to get y = 14/x.\r<BR>\n" );
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document.write( "replace y with 14/x in the second formula to get:\r<BR>\n" );
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document.write( "(1.26 - x) * (14/x + 5) = 14\r<BR>\n" );
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document.write( "distribute the multiplication to get:\r<BR>\n" );
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document.write( "1.26 * 14/x + 5*1.26 - x*14/x - 5x = 14\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "17.65/x + 6.3 - 14 - 5x = 14\r<BR>\n" );
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document.write( "multiply both sides of the equation by x to get:\r<BR>\n" );
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document.write( "17.65 + 6.3x - 14x - 5x^2 = 14x\r<BR>\n" );
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document.write( "subtract 14x from both sides of the equation to get:\r<BR>\n" );
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document.write( "17.65 + 6.3x - 14x - 5x^2 - 14x = 0\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "17.65 - 21.7x - 5x^2 = 0\r<BR>\n" );
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document.write( "reorder the terms in descending order of degree to get:\r<BR>\n" );
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document.write( "-5x^2 - 21.7x + 17.65 = 0\r<BR>\n" );
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document.write( "solve using the quadratic formula to get:\r<BR>\n" );
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document.write( "x = -5.04 or x = .7\r<BR>\n" );
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document.write( "x can't be negative, so x is equal to .7\r<BR>\n" );
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document.write( "x represents time.\r<BR>\n" );
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document.write( "1.26 - x = 1.26 - .7 = .56\r<BR>\n" );
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document.write( "it took him .7 hours to travel the first 14 miles.<BR>\n" );
document.write( "it took him .56 hours to travel the second 4 miles.\r<BR>\n" );
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document.write( "since rate * time = distance, and since x = time and y = rate, you get:\r<BR>\n" );
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document.write( "y * .7 = 14<BR>\n" );
document.write( "solve for y to get y = 14/.7 = 20 miles per hour.\r<BR>\n" );
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document.write( "this makes y + 5 = 25 miles per hour.\r<BR>\n" );
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document.write( "he traveled at 20 miles per hour for the first 14 miles and 25 miles per hour for the second 14 miles.\r<BR>\n" );
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document.write( "the total time it took was .7 hours for the first 14 miles and .56 hours for the second 14 miles for a total of 1.26 hours.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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