document.write( "Question 899314: To paint a room, it takes Mike 75 minutes, Joan 60 minutes, and Kyle 80 minutes when each person works alone. If all three work together, how long will the painting take? \n" ); document.write( "

Algebra.Com's Answer #545323 by josmiceli(19441) $\"\"$ $\"About$

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Add their rates of painting:
\n" ); document.write( "Mike's rate:
\n" ); document.write( "( 1 room ) / ( 75 min )
\n" ); document.write( "Joan's rate:
\n" ); document.write( "( 1 room ) / ( 60 min )
\n" ); document.write( "Kyle's rate:
\n" ); document.write( "( 1 room ) / ( 80 min )
\n" ); document.write( "----------------------
\n" ); document.write( "Let $\"+t+\"$ = time in minutes with
\n" ); document.write( "all 3 painting:
\n" ); document.write( " $\"+1%2F75+%2B1%2F60+%2B+1%2F80+=+1%2Ft+\"$
\n" ); document.write( "Multiply both sides by $\"+5+\"$
\n" ); document.write( " $\"+1%2F15+%2B+1%2F12+%2B+1%2F16+=+5%2Ft+\"$
\n" ); document.write( "Multiply both sides by $\"+240t+\"$
\n" ); document.write( " $\"+16t+%2B+20t+%2B+15t+=+1200+\"$
\n" ); document.write( " $\"+51t+=+1200+\"$
\n" ); document.write( " $\"+t+=+23.53+\"$
\n" ); document.write( "-------------
\n" ); document.write( "with all 3 painting it will take 23.53 min
\n" ); document.write( "-------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2F75+%2B1%2F60+%2B+1%2F80+=+1%2Ft+\"$
\n" ); document.write( " $\"+1%2F75+%2B1%2F60+%2B+1%2F80+=+1%2F23.53+\"$
\n" ); document.write( " $\"+.01333+%2B+.01666+%2B+.0125+=+.0425+\"$
\n" ); document.write( " $\"+.04249+=+.0425+\"$
\n" ); document.write( "close enough\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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