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You can put this solution on YOUR website!
the basic assumption here is that they all work at the same rate.
\n" ); document.write( "the basic formula is rate * number of people who work at the same rate * time = quantity of work.
\n" ); document.write( "that would be n * r * t = q
\n" ); document.write( "the quantity of work in this problem is the weeding of one farm.
\n" ); document.write( "this makes q = 1.
\n" ); document.write( "the number of people who are originally working is 6.
\n" ); document.write( "the rate at which each of the men is working needs to be found.
\n" ); document.write( "it is initially assumed that the men work the full 16 days, so the formula becomes 6 * r * 16 = 1
\n" ); document.write( "now you can solve for r to get r = 1 / (6 * 16) = .0104166667.
\n" ); document.write( "replace r in the original formula to test if this value is good.
\n" ); document.write( "you get 6 * .0104166667 * 16 = 1, confirming the value is good.
\n" ); document.write( "now that you have the rate that each man works at (all assumed to be working at the same rate), you can solve the problem.
\n" ); document.write( "the 6 men work at that rate for 4 days.
\n" ); document.write( "the formula becomes 6 * .0104166667 * 4 = q
\n" ); document.write( "solve for q to get q = .25.
\n" ); document.write( "the 6 men finish 1/4 of the job in 4 days.
\n" ); document.write( "that stands to reason because 4 is 1/4 of 16.
\n" ); document.write( "they have 3/4 of the job left to do, at which time the additional 2 men are added.
\n" ); document.write( "the formula becomes 8 * .0104166667 * t = 3/4.
\n" ); document.write( "solve for t to get t = (3/4) / (8 * .0104166667) = 9 days.
\n" ); document.write( "the total job is finished in 4 + 9 = 13 days.
\n" ); document.write( "that's your solution.\r
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