document.write( "Question 638939: Alan can do a piece of work in 15 days; Bill can do it in 20 days. If Alan works alone on the job for five days, and theb Bill helps hin complete it, how long does Bill work? \n" ); document.write( "

Algebra.Com's Answer #402495 by josmiceli(19441) $\"\"$ $\"About$

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If Alan does a whole job in 15 days, he will do 1/3 of the job
\n" ); document.write( "in 5 days, so 1/3 is done when Bill starts working.
\n" ); document.write( "2/3 of the job is left to do.
\n" ); document.write( "Now add their rates of working to get their rate working together
\n" ); document.write( "In words:
\n" ); document.write( "( 1 job ) / ( 15 days ) + ( 1 job ) / ( 20 days ) = ( 2/3 of a job ) / ( x days )
\n" ); document.write( " $\"+1%2F15+%2B+1%2F20+=+%282%2F3%29+%2F+x+\"$
\n" ); document.write( "Multiply both sides by $\"+60x+\"$
\n" ); document.write( " $\"+4x+%2B+3x+=+120%2F3+\"$
\n" ); document.write( " $\"+7x+=+40+\"$
\n" ); document.write( " $\"+x+=+5.7143+\"$
\n" ); document.write( "Bill works for 5.7143 days
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2F15+%2B+1%2F20+=+%282%2F3%29+%2F+x+\"$
\n" ); document.write( " $\"+.06667+%2B+.05+=+.6667+%2F+5.7143+\"$
\n" ); document.write( " $\"+.116667+=+.6667+%2F+5.7143+\"$
\n" ); document.write( " $\"+.116667%2A5.7143+=+.6667+\"$
\n" ); document.write( " $\"+.666687+=+.6667+\"$
\n" ); document.write( "close enough \n" ); document.write( "

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