document.write( "Question 128209: It takes Tom 3 hours less to paint a fence than it does Jim. If the two boys work together, they can paint the fence in 2 hours. How many hours would each boym working alone need to paint the fence? \n" ); document.write( "

Algebra.Com's Answer #93878 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Add their rates of doing work
\n" ); document.write( "(1 fence) / (Tom's time to paint it) + (1 fence) / (Jim's time to paint it) =
\n" ); document.write( "(1 fence) / (the time it takes them working together)
\n" ); document.write( "Let $\"j\"$ = Jim's time to paint the fence
\n" ); document.write( " $\"1+%2F+%28j+-+3%29+%2B+1+%2F+j+=+1+%2F+2\"$
\n" ); document.write( "multiply both sides by $\"2%2Aj%2A%28j+-+3%29\"$
\n" ); document.write( " $\"2j+%2B+2%28j+-+3%29+=+j%2A%28j+-+3%29\"$
\n" ); document.write( " $\"2j+%2B+2j+-+6+=+j%5E2+-+3j\"$
\n" ); document.write( " $\"j%5E2+-+7j+%2B+6+=+0\"$
\n" ); document.write( " $\"%28j+-+6%29%28j+-+1%29+=+0\"$
\n" ); document.write( "The solutions are $\"j+=+6\"$ and $\"j+=+1\"$
\n" ); document.write( "I'm going to reject $\"j+=+1\"$ as a solution,
\n" ); document.write( "since Tom's time which is $\"j+-+3\"$ would
\n" ); document.write( "be negative.
\n" ); document.write( "Jim's time working alone is 6 hours
\n" ); document.write( "and Tom's time working alone is 3 hours
\n" ); document.write( "check:
\n" ); document.write( " $\"1%2F3+%2B+1%2F6+=+1%2F2\"$
\n" ); document.write( " $\"2%2F6+%2B+1%2F6+=+1%2F2\"$
\n" ); document.write( " $\"3%2F6+=+1%2F2\"$
\n" ); document.write( " $\"1%2F2+=+1%2F2\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

\n" );