document.write( "Question 503738: 2 men and 5 boys can do piece of work in 4 days , while 4 men and 4 boys can do in 3 day. how long would it take one man alone to do it and how many days would it take one boy alone to do it
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Algebra.Com's Answer #339413 by Edwin McCravy(20060) $\"\"$ $\"About$
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2 men and 5 boys can do piece of work in 4 days , while 4 men and 4 boys can do in 3 day. how long would it take one man alone to do it and how many days would it take one boy alone to do it.
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document.write( "Make this chart:\r\n" );
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document.write( "                   Number of          Time             \r\n" );
document.write( "                   jobs done        required        Rate\r\n" );
document.write( "                   or fraction         in            in\r\n" );
document.write( "                     thereof          days        jobs/day\r\n" );
document.write( "1 Man                                \r\n" );
document.write( "1 Boy                                 \r\n" );
document.write( "2 Men                               \r\n" );
document.write( "5 Boys                                 \r\n" );
document.write( "4 Men                                \r\n" );
document.write( "4 Boys                              \r\n" );
document.write( "2 Men and 5 Boys                       \r\n" );
document.write( "4 Men and 4 Boys                     \r\n" );
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document.write( "Fill in 1 for the number of jobs done in each case:\r\n" );
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document.write( "                   Number of          Time\r\n" );
document.write( "                   jobs done        required        Rate\r\n" );
document.write( "                   or fraction         in            in\r\n" );
document.write( "                     thereof          days        jobs/day\r\n" );
document.write( "1 Man                    1            \r\n" );
document.write( "1 Boy                    1            \r\n" );
document.write( "2 Men                    1            \r\n" );
document.write( "5 Boys                   1             \r\n" );
document.write( "4 Men                    1            \r\n" );
document.write( "4 Boys                   1          \r\n" );
document.write( "2 Men and 5 Boys         1            \r\n" );
document.write( "4 Men and 4 Boys         1            \r\n" );
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document.write( "Let M be the time required for 1 man to complete the job\r\n" );
document.write( "Let B be the time required for 1 boy to complete the job\r\n" );
document.write( "Therefore the number of days required for 2 Men will by\r\n" );
document.write( "only half of M that or M/2\r\n" );
document.write( "And the number of days required for 5 boys will be only\r\n" );
document.write( "one-fifth of B or B/5\r\n" );
document.write( "We are given the times in the last two cases.\r\n" );
document.write( "Fill all those in:\r\n" );
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document.write( "                   Number of          Time\r\n" );
document.write( "                   jobs done        required        Rate\r\n" );
document.write( "                   or fraction         in            in\r\n" );
document.write( "                     thereof          days        jobs/day\r\n" );
document.write( "1 Man                    1              M           \r\n" );
document.write( "1 Boy                    1              B           \r\n" );
document.write( "2 Men                    1             M/2          \r\n" );
document.write( "5 Boys                   1             B/5            \r\n" );
document.write( "4 Men                    1             M/4          \r\n" );
document.write( "4 Boys                   1             B/4          \r\n" );
document.write( "2 Men and 5 Boys         1              4           \r\n" );
document.write( "4 Men and 4 Boys         1              3           \r\n" );
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document.write( "Next we fill in the Rates in jobs/day by dividing\r\n" );
document.write( "number of jobs by the number of days. Notice that\r\n" );
document.write( "1 over a fraction is the reciprocal of that fraction:\r\n" );
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document.write( "                   jobs done        required        Rate\r\n" );
document.write( "                   or fraction         in            in\r\n" );
document.write( "                     thereof          days        jobs/day\r\n" );
document.write( "1 Man                    1              M            1/M\r\n" );
document.write( "1 Boy                    1              B            1/B \r\n" );
document.write( "2 Men                    1             M/2           2/M \r\n" );
document.write( "5 Boys                   1             B/5           5/B  \r\n" );
document.write( "4 Men                    1             M/4           4/M \r\n" );
document.write( "4 Boys                   1             B/4           4/B\r\n" );
document.write( "2 Men and 5 Boys         1              4            1/4\r\n" );
document.write( "4 Men and 4 Boys         1              3            1/3\r\n" );
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document.write( "The sum of the rates for 2 Men and 5 Boys must equal to their \r\n" );
document.write( "combined rate, so\r\n" );
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document.write( "2/M + 5/B = 1/4\r\n" );
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document.write( "The sum of the rates for 4 Men and 4 Boys must equal to their \r\n" );
document.write( "combined rate, so\r\n" );
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document.write( "4/M + 4/B = 1/3\r\n" );
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document.write( "So we have this system of equations:\r\n" );
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document.write( "Do not clear of fractions.  Use elimination\r\n" );
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document.write( "Multiply the first equation through by -2\r\n" );
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document.write( "Adding them term by term:\r\n" );
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document.write( "It would take a boy 36 days.\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "It would take one man 18 days.\r\n" );
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document.write( "Edwin
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