document.write( "Question 657201: 6 children and 2 men complete a certain peice of work in 6 days ,each child takes twice the time teken by a man to fifnish the work ,in how many days will 6 men ll finish the work? \n" ); document.write( "

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THE FIFTH GRADER SOLUTION:
\n" ); document.write( "If \"each child takes twice the time taken by a man to finish the work\", then 2 children do the same work as 1 man, and 6 children would do the work of 3 men.
\n" ); document.write( "Then, 6 children and 2 men would do the same work as 3 men and another 2 men, which adds up to 5 men.
\n" ); document.write( "The amount of work done was 5 men times 6 days or $\"5%2A6\"$ man-days.
\n" ); document.write( "Obviously, 6 men working $\"highlight%285%29\"$ days will also finish the same $\"5%2A6\"$ man-days job.
\n" ); document.write( "
\n" ); document.write( "WHAT THE TEACHER EXPECTS,
\n" ); document.write( "I am not exactly sure, because there are many problem-solving recipe books.
\n" ); document.write( "I do not know what recipe your teacher uses, but I will try my best guess.
\n" ); document.write( "The amount of work done by a person or a group (or some sort of machine, divided by the time worked is the rate of work.
\n" ); document.write( " $\"rate=work%2Ftime\"$
\n" ); document.write( "once we know the rate of work, we can calculate work done over a given period of time, or time required to finish a given amount of work
\n" ); document.write( "If one man would take $\"t\"$ days to finish the job by himself, then a child would take $\"2t\"$ days.
\n" ); document.write( "A man's rate of work would be $\"1%28job%29%2F%28t%28days%29%29=1%2Ft\"$ , in jobs per day.
\n" ); document.write( "(We could call that the rate of work of a man, $\"r=1%2Ft\"$ , in jobs per day, and we would save ourselves from writing so many denominators).
\n" ); document.write( "A child's rate of work would be $\"1%28job%29%2F%282t%28days%29%29=1%2F2t\"$
\n" ); document.write( "The rate of work for a group would be found adding the rates for all the members of the group.
\n" ); document.write( "The rate of work for 6 men would be $\"6%2A%281%2Ft%29=6%2Ft\"$ .
\n" ); document.write( "The rate of work for 2 men and 6 children would be
\n" ); document.write( " $\"2%2A%281%2Ft%29%2B6%2A%281%2F2t%29=2%2Ft%2B3%2Ft=5%2Ft\"$
\n" ); document.write( "The group of 2 men and 6 children completed 1 job in 6 days, so
\n" ); document.write( " $\"6%2A%285%2Ft%29=1\"$ job
\n" ); document.write( "The group of 6 mean would complete the same job in $\"x\"$ days, so
\n" ); document.write( " $\"x%2A%285%2Ft%29=6%2A%285%2Ft%29\"$
\n" ); document.write( "Multiplying both sides times $\"t\"$ , which we know is not zero,
\n" ); document.write( " $\"x%2A%285%2Ft%29=6%2A%285%2Ft%29\"$ --> $\"5x=6%2A5\"$ --> $\"highlight%28x=5%29\"$ days. \n" ); document.write( "

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