document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=884691>Question 884691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If one man or two women or three boys can finish a work in 66days then how many days will one man, one woman and one boy together take to finish the same work? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #534581 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=534581\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> one man or 2 women or 3 boys can finish a job in 66 days.\r<BR>\n" );
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document.write( "the formula to use is:<BR>\n" );
document.write( "R * P * T = Q<BR>\n" );
document.write( "R = rate per person.<BR>\n" );
document.write( "P = number of persons<BR>\n" );
document.write( "T = time<BR>\n" );
document.write( "Q = quantity of work.\r<BR>\n" );
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document.write( "set Q = 1 piece of work.<BR>\n" );
document.write( "set T = 66<BR>\n" );
document.write( "set P = the number of persons<BR>\n" );
document.write( "you will want to solve for R which will give you the rate per person.\r<BR>\n" );
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document.write( "for the man:<BR>\n" );
document.write( "R * P * T = Q becomes:<BR>\n" );
document.write( "R * 1 * 66 = 1<BR>\n" );
document.write( "divide both sides of this equation by 66 and you get:<BR>\n" );
document.write( "R * 1 =  1/66<BR>\n" );
document.write( "divide both sides of this equation by 1 to get:<BR>\n" );
document.write( "R = 1/66<BR>\n" );
document.write( "one man can finish 1/66 of the job in 1 day.\r<BR>\n" );
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document.write( "for the women:<BR>\n" );
document.write( "R * P * T = Q becomes:<BR>\n" );
document.write( "R * 2 * 66 = 1<BR>\n" );
document.write( "divide both sides of this equation by 66 and you get:<BR>\n" );
document.write( "R * 2 = 1/66<BR>\n" );
document.write( "divide both sides of this equation by 2 to get:<BR>\n" );
document.write( "R = 1/132<BR>\n" );
document.write( "one woman can finish 1/132 of the job in 1 day.\r<BR>\n" );
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document.write( "for the boys:<BR>\n" );
document.write( "R * P * T = Q becomes:<BR>\n" );
document.write( "R * 3 * 66 = 1<BR>\n" );
document.write( "divide both sides of this equation by 66 and you get:<BR>\n" );
document.write( "R * 3 = 1/66<BR>\n" );
document.write( "divide both sides of this equation by 3 to get:<BR>\n" );
document.write( "R = 1/198<BR>\n" );
document.write( "one boy can finish 1/198 of the job in 1 day.\r<BR>\n" );
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document.write( "the question is:<BR>\n" );
document.write( "how many days will one man, one woman and one boy together take to finish the same work?\r<BR>\n" );
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document.write( "the rate of one man is 1/66<BR>\n" );
document.write( "the rate of one woman is 1/132<BR>\n" );
document.write( "the rate of 1 boy is 1/198\r<BR>\n" );
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document.write( "working together their rates are additive.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "R * P * T = 1<BR>\n" );
document.write( "Since P is equal to 1 all around, this formula becomes:<BR>\n" );
document.write( "R * T = 1<BR>\n" );
document.write( "The R in this case is the overall rate of the 3 people working together.<BR>\n" );
document.write( "we get:<BR>\n" );
document.write( "R = (1/66 + 1/132 + 1/198) which is equivalent to:<BR>\n" );
document.write( "R = (6/396 + 3/396 + 2/396) which is equivalent to:<BR>\n" );
document.write( "R = 11/396\r<BR>\n" );
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document.write( "R * T = 1 becomes:<BR>\n" );
document.write( "11/396 * T = 1<BR>\n" );
document.write( "divide both sidesof this eqution by (11/396) and you get:<BR>\n" );
document.write( "T = 1 / (11/396) = 1 * (396/11) = 396/11 = 36 days.\r<BR>\n" );
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document.write( "1 man and 1 woman and 1 boy, working together, can complete the work in 36 days.\r<BR>\n" );
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document.write( "the man will have completed 1/66 * 36 = 36/66 of the work in 36 days.<BR>\n" );
document.write( "the woman will have completed 1/132 * 36 = 36/132 of the work in 36 days.<BR>\n" );
document.write( "the boy will have completed 1/198 * 36 = 36/198 of the work in 36 days.\r<BR>\n" );
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document.write( "add these up together and you should get 1.<BR>\n" );
document.write( "36/66 + 36/132 + 56/198 is equivalent to:<BR>\n" );
document.write( "(36*6 + 36*3 + 36*2) / 396 which is equivalent to:<BR>\n" );
document.write( "(216 + 108 + 72) / 396 which is equivalent to:<BR>\n" );
document.write( "396/396 which is equivalent to 1.\r<BR>\n" );
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document.write( "solution is correct.<BR>\n" );
document.write( "answer is 36 days.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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