document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204175>Question 1204175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> P can complete a task in x days while Q takes (x + 12) days to do the same task.<BR>\n" );
document.write( "a) What fraction of the task can each of them complete in a day?<BR>\n" );
document.write( "b) If both of them work together, they can<BR>\n" );
document.write( "complete the task in 8 days. Find x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840251 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=840251\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let p = the rate that P works per day.<BR>\n" );
document.write( "let q = the rate that Q works per day.\r<BR>\n" );
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document.write( "rate * time = quantity.\r<BR>\n" );
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document.write( "for P, you get p * x = 1, resulting in p = 1/x<BR>\n" );
document.write( "for Q, you get q * (x + 12) = 1, resulting in q = 1/(x + 12).\r<BR>\n" );
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document.write( "you are given that they can both complete the task in 8 days when working together.<BR>\n" );
document.write( "the equation for that is 8 * (p + q) = 1<BR>\n" );
document.write( "simplify to get 8p + 8q = 1\r<BR>\n" );
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document.write( "since p = 1/x and q = 1/(x + 12), you get:<BR>\n" );
document.write( "8 * 1/x + 8 * 1/(x + 12) = 1<BR>\n" );
document.write( "simplify to get 8/x + 8/(x + 12) = 1<BR>\n" );
document.write( "multiply both sides of this equation by x * (x + 12) to get:<BR>\n" );
document.write( "8 * (x + 12) + 8 * x = x * (x + 12)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "8x + 96 + 8x = x^2 + 12x<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "16x + 96 = x^2 + 12x<BR>\n" );
document.write( "subtract the left side of the equation from both sides of the equation to get:<BR>\n" );
document.write( "0 = x^2 + 12x - 16x - 96<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "0 = x^2 - 4x - 96<BR>\n" );
document.write( "solve this quadratic equation to get:<BR>\n" );
document.write( "x = 12 or x = -8.\r<BR>\n" );
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document.write( "since x has to be positive, then x = 12.<BR>\n" );
document.write( "since p = 1/x, then p = 1/12<BR>\n" );
document.write( "since q = 1/(x + 12), then q = 1/24\r<BR>\n" );
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document.write( "since 8p + 8q = 1, then replace p and q with their respective values to get:<BR>\n" );
document.write( "8 * 1/12 + 8 * 1/24 = 1<BR>\n" );
document.write( "simplify to get 8/12 + 8/24 = 1<BR>\n" );
document.write( "simplify further to get 1 = 1, confirming the value of p and q are good.\r<BR>\n" );
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document.write( "answers to your questions are:\r<BR>\n" );
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document.write( "a) What fraction of the task can each of them complete in a day?\r<BR>\n" );
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document.write( "P can complete 1/12 of the task in one day.<BR>\n" );
document.write( "Q can complete 1/24 of the taxk in one day.\r<BR>\n" );
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document.write( "b) If both of them work together, they can complete the task in 8 days. Find x.\r<BR>\n" );
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document.write( "x is equal to 12.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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