document.write( "Question 887869: If it takes 2 days for 5 workers to finish painting a wall at a rate of 6 hours per day, then how long will it take 7 workers to finish painting a wall at a rate of 7 hours per day? \n" ); document.write( "

Algebra.Com's Answer #536889 by Edwin McCravy(20056) $\"\"$ $\"About$

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If it takes 2 days for 5 workers to finish painting a wall at a rate of 6 hours
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document.write( "First of all 2 days at 6 hours per day is 12 hours.\r\n" );
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document.write( "So first of all we'll pretend the problem just speaks of hours like this:\r\n" );
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\n" ); document.write( "It takes 12 hours for 5 workers to finish painting a wall. How many hours
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document.write( "The least common multiple of 5 workers and 7 workers is 35 workers.\r\n" );
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document.write( "35 workers is 7 times 5, so 35 workers can finish painting 7 walls in 12 hours.\r\n" );
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document.write( "7 workers is only  as many as 35, so it will take 7 workers 5 times as long\r\n" );
document.write( "or 60 hours to paint 7 walls.  So to paint only 1 wall will take only th as\r\n" );
document.write( "long as it takes to paint 7 walls.  th of 60 hours is or  or  hours.  \r\n" );
document.write( "So they'll work 1 7-hour day and will finish after  hours on the\r\n" );
document.write( "second day.\r\n" );
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document.write( "You can also use the worker-time-job formula, which is:\r\n" );
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document.write( "where\r\n" );
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document.write( "W₁ = the number of workers in the first situation.\r\n" );
document.write( "T₁ = the number of time units (hours in this case) in the first situation.\r\n" );
document.write( "J₁ = the number of jobs in the first situation.\r\n" );
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document.write( "W₂ = the number of workers in the second situation.\r\n" );
document.write( "T₂ = the number of time units (hours in this case) in the second situation.\r\n" );
document.write( "J₂ = the number of jobs in the second situation.\r\n" );
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document.write( "W₁ =  5             W₂ = 7     \r\n" );
document.write( "T₁ = 12             T₂ = the unknown quantity \r\n" );
document.write( "J₁ =  1             J₂ = 1\r\n" );
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document.write( " hours.  So they'll work 1 7-hour day and will finish after\r\n" );
document.write( " hours on the second day.\r\n" );
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document.write( "Edwin

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