document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1095128>Question 1095128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> three men can individually do a job in 5,6 and 7 hours respectively . what fractions of the entire job is done by the three men together in 1 hour ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #709695 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=709695\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = quantity\r<BR>\n" );
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document.write( "the quantity is equal to 1 job.\r<BR>\n" );
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document.write( "therefore rate * time = 1\r<BR>\n" );
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document.write( "for the first person, the equation becomes rate * 5 = 1<BR>\n" );
document.write( "rate for the first person is 1/5 of the job in 1 hour.\r<BR>\n" );
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document.write( "for the second person, the equation becomes rate * 6 = 1<BR>\n" );
document.write( "rate for the second person is 1/6 of the job in 1 hour.,\r<BR>\n" );
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document.write( "for the third person, the equation becomes rate * 7 = 1<BR>\n" );
document.write( "rate for the third person is 1/7 of the job in 1 hour.\r<BR>\n" );
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document.write( "when all 3 persons work together, their rates are additive.\r<BR>\n" );
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document.write( "their combined rate is (1/5 + 1/6 + 1/7) of the job in 1 hour.\r<BR>\n" );
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document.write( "place (1/5 + 1/6 + 1/7) under the common denominator of 210 and the combined rate becomes (42 + 35 + 30) / 210 = 107/210 of the job in 1 hour.\r<BR>\n" );
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document.write( "their combined rate is 107/210 of the job in 1 hour.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "to determine how long it takes to complete the job, you get:\r<BR>\n" );
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document.write( "r * t = q becomes 107/210 * t = 1\r<BR>\n" );
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document.write( "solve for t to get t = 1 / (107/210) = 1 * 210/107 = 210/107 hours.\r<BR>\n" );
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document.write( "the first person can do the job in 5 hours, therefore his rate is 1/5 of the job in 1 hour.<BR>\n" );
document.write( "multiply that by 210/107 hours and he completes 1/5 * 210/107 = 42/107 of the job in 210/107 hours.\r<BR>\n" );
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document.write( "the second person can do the job in 6 hours, therefore his rate is 1/6 of the job in 1 hour.<BR>\n" );
document.write( "multiply that by 210/107 hours and he completes 1/6 * 210/107 = 35/107 of the job in 210/107 hours.\r<BR>\n" );
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document.write( "the third person can do the job in 7 hours, therefore his rate is 1/7 of the job in 1 hour.<BR>\n" );
document.write( "multiply that by 210/107 hours and he completes 1/7 * 210/107 = 30/107 of the job in 210/107 hours.\r<BR>\n" );
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document.write( "add up the contribution of each person and you get 42/107 + 35/107 + 30/107 = 107/107 of the job in 210/107 hours.\r<BR>\n" );
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document.write( "107/107 is equal to 1, therefore the whole job is completed in 210/107 hours.\r<BR>\n" );
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document.write( "210/107 hours is equal to 1.962616822 hours in decimal form.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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