document.write( "Question 535406: Nicole can paint a room in six hours, Alexandra can paint a room in 5 hours, and Liana can paint a room in 4 hours. If all three work together, how long will it take them to paint the room? \n" ); document.write( "

Algebra.Com's Answer #351889 by josmiceli(19441) $\"\"$ $\"About$

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Add their rates of painting
\n" ); document.write( "( 1 room / 6 hrs ) + ( 1 room / 5 hrs ) + ( 1 room / 4 hrs ) = 1 room / x hrs
\n" ); document.write( " $\"+1%2F6+%2B+1%2F5+%2B+1%2F4+=+1%2Fx+\"$
\n" ); document.write( "Multiply both sides by $\"60x\"$
\n" ); document.write( " $\"+10x+%2B+12x+%2B+15x+=+60+\"$
\n" ); document.write( " $\"+37x+=+60+\"$
\n" ); document.write( " $\"+x+=+60%2F37+\"$
\n" ); document.write( " $\"+x+=+1.622+\"$ hrs
\n" ); document.write( " $\"+.622%2A60+=+37.3+\"$
\n" ); document.write( "It will take them 1 hr and 37 min
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2F6+%2B+1%2F5+%2B+1%2F4+=+1%2Fx+\"$
\n" ); document.write( " $\"+.1666+%2B+.2+%2B+.25+=+.6166+\"$
\n" ); document.write( " $\"+.6166+=+.6166+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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