document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1000927>Question 1000927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer can plow a field in 4 days by using a tractor. A hired hand can plow the same field in 6 days by using a smaller tractor. How many days will be required for the plowing 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 #618275 by </B><A HREF=/tutors/aboutme.mpl?userid=szk17><B>szk17(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=szk17><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=618275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Imagine that the field has an area A given in square feet (the specific unit doesn't matter but it will help understand). Each tractor will cover the field at a different rate (because they operate at different speeds, etc) expressed in square feet per day. For example, 500 square feet/day means the tractor would only complete 500 square feet in one day. If we divide the area of the field A by the rate covered by a given tractor, we get the total time it takes to process the entire field.\r<BR>\n" );
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document.write( "For tractor 1:\r<BR>\n" );
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document.write( "A/rate1 = 4 days                    \r<BR>\n" );
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document.write( "For tractor 2:\r<BR>\n" );
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document.write( "A/rate2 = 6 days\r<BR>\n" );
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document.write( "Quick dimensional analysis check: square feet / (square feet / day) = days \r<BR>\n" );
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document.write( "Express the equations in terms of A, the quantity that relates to both events.\r<BR>\n" );
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document.write( "A = 4 days x rate1 <BR>\n" );
document.write( "A = 6 days x rate2\r<BR>\n" );
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document.write( "Now, the area A is the same so we can do:\r<BR>\n" );
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document.write( "4 days x rate1 = 6 days x rate2  <BR>\n" );
document.write( "rate2 = (4/6) x rate1 \r<BR>\n" );
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document.write( "rate2 = (2/3) x rate1\r<BR>\n" );
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document.write( "Thus, we now know how the performances of the tractors relate to each other.\r<BR>\n" );
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document.write( "If both tractors work together, the number of days is still the area of the field divided by the rate. However, this time, you use two rates!\r<BR>\n" );
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document.write( "time for combined performance = A / (rate1 + rate2)<BR>\n" );
document.write( "                              = A / (rate1 + (2/3) x rate1)<BR>\n" );
document.write( "                              = A / ((5/3) x rate1)\r<BR>\n" );
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document.write( "                              = (3/5) x (A/rate1)\r<BR>\n" );
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document.write( "Remember that A/rate1 = 4 days, so we get:\r<BR>\n" );
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document.write( "                              = (3/5) x 4 days = 2.4 days\r<BR>\n" );
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document.write( "There's an equation you can use or memorize to work such problems but it's better to know what's going on.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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