document.write( "Question 745794: father and a his son can dig a well if the father works 6 hours and his son works 12 hours or they can do its if the father works 9 hours and the son works 8 hours. How long will it take for the son to dig the well alone? \n" ); document.write( "

Algebra.Com's Answer #454010 by josgarithmetic(39617) $\"\"$ $\"About$

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x = father's rate
\n" ); document.write( "y = son's rate
\n" ); document.write( "Those rates are in jobs/hour
\n" ); document.write( "1 job is digging the well.\r
\n" ); document.write( "\n" ); document.write( "These two ways will complete 1 job:
\n" ); document.write( " $\"x%2A6%2By%2A12\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x%2A9%2By%2A8\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "They each equal 1 job, so we have
\n" ); document.write( " $\"x%2A6%2By%2A12=1\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x%2A9%2By%2A8=1\"$
\n" ); document.write( "Two equations with two unknown variables to solve.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Suggestion is multiply the first by 3, multiply the second by 2, and subtract one resulting equation from the other resulting equation. Here is the initial part:\r
\n" ); document.write( "\n" ); document.write( " $\"18x%2B36y=3+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"18x%2B16y=2\"$
\n" ); document.write( "and you do first minus second and obtain 20y=1, so $\"highlight%28y=1%2F20%29\"$ , and ....\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(Looks like the son does 1 job in 20 hours, or works for 20 hours to do the job alone, himself.) \n" ); document.write( "

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