document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1013984>Question 1013984</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A takes 10 more days to do a job than B they both do a job in 12 days. in how many days B will take to complete the work if he works alone?? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #630289 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=630289\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> general formula is R * T = Q<BR>\n" );
document.write( "R = rate<BR>\n" );
document.write( "T = time<BR>\n" );
document.write( "Q = quantity\r<BR>\n" );
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document.write( "Q = 1 job.<BR>\n" );
document.write( "formula becomes R * T = 1\r<BR>\n" );
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document.write( "they can both do the job in 12 days.<BR>\n" );
document.write( "formula for both becomes R * 12 = 1<BR>\n" );
document.write( "solve for R to get:<BR>\n" );
document.write( "R for both = 1/12\r<BR>\n" );
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document.write( "A takes 10 more days to do the job than B when both work alone.\r<BR>\n" );
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document.write( "T for A = T + 10<BR>\n" );
document.write( "T for B = T\r<BR>\n" );
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document.write( "formula for A = R * (T + 10) = 1<BR>\n" );
document.write( "formula for B = R * T = 1\r<BR>\n" );
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document.write( "solve for R to get:\r<BR>\n" );
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document.write( "rate for A = 1/(T+10)<BR>\n" );
document.write( "rate for B = 1/T\r<BR>\n" );
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document.write( "when they both work together, their rates are additive.\r<BR>\n" );
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document.write( "R for both = 1/(T+10) + 1/T\r<BR>\n" );
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document.write( "since R for both = 1/12. we get:<BR>\n" );
document.write( "1/(T+10) + 1/T = 1/12\r<BR>\n" );
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document.write( "we can use this formula to solve for T.<BR>\n" );
document.write( "the T that we will be solving for is the T for A and the T for B.<BR>\n" );
document.write( "multiply both sides of this equation by T * (T + 10) to get:<BR>\n" );
document.write( "T + (T + 10) = 1/12 * T * (T + 10)<BR>\n" );
document.write( "simplify this equation to get:<BR>\n" );
document.write( "T + T + 10 = 1/12 * (T^2 + 10T)<BR>\n" );
document.write( "combine like terms and simplify further to get:<BR>\n" );
document.write( "2T + 10 = 1/12 * T^2 + 1/12 * 10T<BR>\n" );
document.write( "multiply both sides of this equation by 12 to get:<BR>\n" );
document.write( "24T + 120 = T^2 + 10T<BR>\n" );
document.write( "subtract 24T + 120 from both sides of this equation to get:<BR>\n" );
document.write( "0 = T^2 + 10T - 24T - 120<BR>\n" );
document.write( "combine like terms and commute the equation to get:<BR>\n" );
document.write( "T^2 - 14T - 120 = 0<BR>\n" );
document.write( "factor this quadratic to get:<BR>\n" );
document.write( "(T + 10) * (T - 20) = 0<BR>\n" );
document.write( "solve for T to get:<BR>\n" );
document.write( "T = -10 or T = 20<BR>\n" );
document.write( "T can't be negative, so T = 20 is the solution.\r<BR>\n" );
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document.write( "T = 20 is the time for B.<BR>\n" );
document.write( "T = 30 is the time for A because A takes 10 more days to complete the job on his own than B does.\r<BR>\n" );
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document.write( "the solution to your problem is that B takes 20 days to complete the job on his own.\r<BR>\n" );
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document.write( "you should confirm your answer is correct.\r<BR>\n" );
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document.write( "you do this by replacing T for A with 30 and T for B with 20 and solving for R for A and B individually and then solving for both to see if everything checks out.\r<BR>\n" );
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document.write( "we now know that T for A is 30 and Q is 1.<BR>\n" );
document.write( "we can solve for R for A to get R = 1/30.\r<BR>\n" );
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document.write( "similarly we can solve for R for B to get R = 1/20\r<BR>\n" );
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document.write( "the RT = Q equation for A becomes 1/30 * 30 = 1 which results in 1 = 1 which confirms the solution is good.\r<BR>\n" );
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document.write( "the RT = Q equation for B becomes 1/20 * 20 = 1 which results in 1 = 1 which confirms the solution is good.\r<BR>\n" );
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document.write( "the RT = Q equation for A and B together becomes (1/30 + 1/20) * 12 = 1.<BR>\n" );
document.write( "this is because, when they work together, their rates are additive and we already know that they take 12 days to complete the job when they work together.<BR>\n" );
document.write( "start with:<BR>\n" );
document.write( "(1/30 + 1/20) * 12 = 1<BR>\n" );
document.write( "multiply both sides of this equation by 20*30 to get:<BR>\n" );
document.write( "(20 + 30) * 12 = 20 * 30<BR>\n" );
document.write( "combine like terms and simplify to get:<BR>\n" );
document.write( "50 * 12 = 600<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "50 * 12 = 600 becomes 600 = 600 which confirms the solution is good.\r<BR>\n" );
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document.write( "the solution is:\r<BR>\n" );
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document.write( "it will take B 20 days to complete the job if he works alone.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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