document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139833>Question 1139833</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A carabao can plough a farmer's land in 6 hours. A tractor can plough the land in 4 hours. The farmer used the carabao to plough the land for 2 hours, after which, another farmer decided to help him using the tractor. How long did it take the farmers tofinish ploughing  the land? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760330 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=760330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r * t = q\r<BR>\n" );
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document.write( "r is the rate<BR>\n" );
document.write( "t is the time<BR>\n" );
document.write( "q is the quantity.\r<BR>\n" );
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document.write( "the quantity in this case is one ploughed field.\r<BR>\n" );
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document.write( "the carabao can do it in 6 hours, therefore r * t = q becomes r * 6 = 1.<BR>\n" );
document.write( "solve for r to get r = 1/6.\r<BR>\n" );
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document.write( "the tractor can do it in 4 hours, therefore r * t = q becomes r * 4 = 1.<BR>\n" );
document.write( "solve for r to get r = 1/4.\r<BR>\n" );
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document.write( "the rate of the carabao is 1/6 of the field in 1 hour.<BR>\n" );
document.write( "the rate of the tractor is 1/4 of the field in 1 hour.\r<BR>\n" );
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document.write( "the farmer uses the carabao to plough the field for 2 hours.\r<BR>\n" );
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document.write( "r * t = q becomes 1/6 * 2 = q.<BR>\n" );
document.write( "solve for q to get q = 1/6 * 2 = 1/6 = 1/3.\r<BR>\n" );
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document.write( "in 2 hours, the farmer has ploughed 1/3 of the field.\r<BR>\n" );
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document.write( "that leave 2/3 of the field to still be ploughed.\r<BR>\n" );
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document.write( "another farmer decides to help him using the tractor.\r<BR>\n" );
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document.write( "the last 2/3 of the field is then ploughed using the carabao and the tractor.\r<BR>\n" );
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document.write( "when both are used, their rates are additive.\r<BR>\n" );
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document.write( "the formula of r * t = q becomes (1/6 + 1/4) * t = 2/3\r<BR>\n" );
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document.write( "simplify to get 5/12 * t = 2/3\r<BR>\n" );
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document.write( "solve for t to get t = 2/3 * 12/5 = 8/5.\r<BR>\n" );
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document.write( "the remaining 2/3 of the field is ploughed in 8/5 = 1 and 3/5 hours.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "r * t = q becomes 1/6 * 2 + 5/12 * 8/5 = q<BR>\n" );
document.write( "1/6 * 2 is with the carabao only.<BR>\n" );
document.write( "5/12 * 8/5 is with both the carabao and the tractor.<BR>\n" );
document.write( "solve for q to get q = 1<BR>\n" );
document.write( "the whole field is ploughed in 2 hours and 8/5 hours = 3 and 3/5 hours.<BR>\n" );
document.write( "that was 2 hours using the carabao and 1 and 3/5 hours using both the tractor and the carabao.\r<BR>\n" );
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document.write( "any questions, write to dtheophilis@gmail.com\r<BR>\n" );
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document.write( " </SPAN>\n" );
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