document.write( "Question 499228: Mike, Joe and Bill are painting a fence. The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours, or if Mike and Joe work together for 2 hours and Bill works alone for 5 hours, or if Mike works alone for 6 hours, Joe works alone for 2 hours and Bill works alone for 1 hour. How much time does it take each man working alone to complete the painting. \n" ); document.write( "

Algebra.Com's Answer #337676 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Mike, Joe and Bill are painting a fence.
\n" ); document.write( " The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours, or if Mike and Joe work together for 2 hours and Bill works alone for 5 hours, or if Mike works alone for 6 hours, Joe works alone for 2 hours and Bill works alone for 1 hour.
\n" ); document.write( " How much time does it take each man working alone to complete the painting.
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each scenario, let the completed job = 1
\n" ); document.write( ":
\n" ); document.write( "The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours,\"
\n" ); document.write( " $\"4%2Fm\"$ + $\"4%2Fj\"$ + $\"2%2Fb\"$ = 1
\n" ); document.write( ":
\n" ); document.write( "\"if Mike and Joe work together for 2 hours and Bill works alone for 5 hours,\"
\n" ); document.write( " $\"2%2Fm\"$ + $\"2%2Fj\"$ + $\"5%2Fb\"$ = 1
\n" ); document.write( ":
\n" ); document.write( "\"if Mike works alone for 6 hours, Joe works alone for 2 hours and Bill works alone for 1 hour.\"
\n" ); document.write( " $\"6%2Fm\"$ + $\"2%2Fj\"$ + $\"1%2Fb\"$ = 1
\n" ); document.write( ":
\n" ); document.write( "We are going to use elimination here multiply the 2nd eq by 2, subtract the 1st equation
\n" ); document.write( " $\"4%2Fm\"$ + $\"4%2Fj\"$ + $\"10%2Fb\"$ = 2
\n" ); document.write( " $\"4%2Fm\"$ + $\"4%2Fj\"$ + $\"2%2Fb\"$ = 1
\n" ); document.write( "---------------------------------------subtraction eliminates m and j, find b
\n" ); document.write( " $\"8%2Fb\"$ = 1
\n" ); document.write( "b = 8 hrs for Bill alone
\n" ); document.write( ":
\n" ); document.write( "In the 2nd equation replace b with 8
\n" ); document.write( " $\"2%2Fm\"$ + $\"2%2Fj\"$ + $\"5%2F8\"$ = 1
\n" ); document.write( " $\"2%2Fm\"$ + $\"2%2Fj\"$ = 1 - $\"5%2F8\"$
\n" ); document.write( " $\"2%2Fm\"$ + $\"2%2Fj\"$ = $\"3%2F8\"$
\n" ); document.write( "Do the same with the 3rd equation
\n" ); document.write( " $\"6%2Fm\"$ + $\"2%2Fj\"$ + $\"1%2F8\"$ = 1
\n" ); document.write( " $\"6%2Fm\"$ + $\"2%2Fj\"$ = $\"7%2F8\"$
\n" ); document.write( "use these two equation for elimination
\n" ); document.write( " $\"6%2Fm\"$ + $\"2%2Fj\"$ + $\"7%2F8\"$
\n" ); document.write( " $\"2%2Fm\"$ + $\"2%2Fj\"$ + $\"3%2F8\"$
\n" ); document.write( "----------------------------------Subtraction eliminates j, find m
\n" ); document.write( " $\"4%2Fm\"$ = $\"4%2F8\"$
\n" ); document.write( "m = 8 hrs for Mike alone
\n" ); document.write( ":
\n" ); document.write( "find j using eq: $\"2%2Fm\"$ + $\"2%2Fj\"$ = $\"3%2F8\"$ , replace m with 8
\n" ); document.write( " $\"2%2F8\"$ + $\"2%2Fj\"$ = $\"3%2F8\"$
\n" ); document.write( " $\"2%2Fj\"$ = $\"3%2F8\"$ - $\"2%2F8\"$
\n" ); document.write( " $\"2%2Fj\"$ = $\"1%2F8\"$
\n" ); document.write( "Cross multiply
\n" ); document.write( "j = 2*8
\n" ); document.write( "j = 16 hrs for Joe alone
\n" ); document.write( ":
\n" ); document.write( "to do the job alone: m = 8 hrs, j = 16 hrs, b = 8hrs
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Confirm this in the 1st equation
\n" ); document.write( " $\"4%2F8\"$ + $\"4%2F16\"$ + $\"2%2F8\"$ = 1
\n" ); document.write( "which is
\n" ); document.write( " $\"4%2F8\"$ + $\"2%2F8\"$ + $\"2%2F8\"$ = 1
\n" ); document.write( "
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