document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065767>Question 1065767</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Out of the work man x and y,x is twice as good as y to perform the work assigned to them.If x can finish the assigned work in 40 days less than y,then in how many days they together can finish the work if they work together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #680940 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=680940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x can finish the work in 40 days less than y.<BR>\n" );
document.write( "x works twice as fast as y, if i understood you correctly.\r<BR>\n" );
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document.write( "if we let z = the rate of y, then 2z = the rate of x.\r<BR>\n" );
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document.write( "rate * time = quantity of work produced.\r<BR>\n" );
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document.write( "quantity of work produced = 1 job.\r<BR>\n" );
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document.write( "if we let q = the time it takes y to finish the work, then q - 40 is the time it takes x to finish the work.\r<BR>\n" );
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document.write( "when y works, the formula becomes z * q = 1\r<BR>\n" );
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document.write( "when x works, the formula becomes 2z * (q-40) = 1\r<BR>\n" );
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document.write( "if we solve both of these formulas for z, we get:\r<BR>\n" );
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document.write( "z = 1/q and z = 1/(2 * (q-40))\r<BR>\n" );
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document.write( "simplify to get z = 1/q and z = 1/(2q-80)\r<BR>\n" );
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document.write( "this means that 1/q = 1/(2q-80)\r<BR>\n" );
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document.write( "cross multiply to get 2q-80 = q\r<BR>\n" );
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document.write( "subtract q from both sides of this equaiton to get q-80 = 0\r<BR>\n" );
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document.write( "solve for q to get q = 80\r<BR>\n" );
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document.write( "when y works, you get zq = 1 which becomes 80z = 1 which becomes z = 1/80.\r<BR>\n" );
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document.write( "when x works, you get 2z(q-40) = 1 which becomes 2z(80-40) = 1 which becomes 2z*40 = 1 which becomes 2z = 1/40.\r<BR>\n" );
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document.write( "remember now, that the rate of y is z and the rate of x is 2z.\r<BR>\n" );
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document.write( "the rate of x is 1/80 of the job in 1 day.\r<BR>\n" );
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document.write( "the rate of y is 1/40 of the job in 1 day.\r<BR>\n" );
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document.write( "when they work together, their rates are additive, so you get:\r<BR>\n" );
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document.write( "(1/80 + 1/40) * q = 1\r<BR>\n" );
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document.write( "q in this case is the time it takes when they are working together.\r<BR>\n" );
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document.write( "simplify to get 3/80 * q = 1\r<BR>\n" );
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document.write( "solve for q to get q = 80/3 = 26 and 2/3 days.\r<BR>\n" );
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document.write( "your answer should be that they take 26 and 2/3 days to complete the job when they work together. if i understood your problem correctly.\r<BR>\n" );
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document.write( "when x works alone, he takes 40 days to complete the job.<BR>\n" );
document.write( "when y works alone, he takes 80 days to complete the job.\r<BR>\n" );
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document.write( "x takes 40 days less than y to complete the job, so that part checks out.\r<BR>\n" );
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document.write( "the rate of x is 1/40 of the job in one day while the rate of y is 1/80 of the job in 1 day, so the rate of x is twice the rate of y, so that part checks out as well.\r<BR>\n" );
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document.write( "i believe that 26 and 2/3 days to complete the job when they work together is the solution you are looking for.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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