document.write( "Question 266485: A new computer can process a company’s monthly payroll in 1 hour less time than the old computer. To really save time, the manager used both computers and finished the payroll in 3 hours. How long would it take the new computer to do the payroll by itself? \n" ); document.write( "

Algebra.Com's Answer #195800 by ptaylor(2198) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let x=amount of time it takes the old computer working alone to do the payroll
\n" ); document.write( "Then the old computer works at the rate of 1/x of the payroll per hour
\n" ); document.write( "We are told that the new computer working alone can do the payroll in x-1 hours
\n" ); document.write( "Then the new computer works at the rate of 1/(x-1) of the payroll per hour
\n" ); document.write( "Together the two computers work at the rate of 1/x + 1/(x-1) of the payroll per hour
\n" ); document.write( "We are also told that when both computers are used, they can do the job in 3 hours.
\n" ); document.write( "So, together the computers work at the rate of 1/3 of the payroll per hour
\n" ); document.write( "So, our equation to solve is:
\n" ); document.write( "1/x + 1/(x-1)=1/3 multiply each term by 3*x*(x-1)
\n" ); document.write( "3(x-1)+3x=x(x-1) simplify
\n" ); document.write( "3x-3+3x=x^2-x or
\n" ); document.write( "6x-3=x^2-x subtract 6x from and add 3 to both sides
\n" ); document.write( "6x-6x-3+3=x^2-x-6x+3 collect like terms
\n" ); document.write( "x^2-7x+3=0-----------Quadratic in standard form; solve using the quadratic formula
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"x+=+%287%2B-+sqrt%28+49-12+%29%29%2F%282%29+\"$
\n" ); document.write( " $\"x+=+%287%2B-+sqrt%2837%29%29%2F%282%29+\"$
\n" ); document.write( " $\"x+=+%287%2B-6.1%29%2F%282%29+\"$
\n" ); document.write( " $\"x+=+%287%2B6.1%29%2F%282%29+\"$
\n" ); document.write( " $\"x+=+6.55hr+\"$ ------------------time it takes the old computer to do the payroll working alone
\n" ); document.write( " $\"x-1=6.55-1=5.55hr+\"$ -----time it would take the new computer working alone\r
\n" ); document.write( "\n" ); document.write( "Another possible solution is:
\n" ); document.write( " $\"x+=+%287-6.1%29%2F%282%29+\"$
\n" ); document.write( " $\"x+=+0.45hr\"$ ---- time it would take the old computer to do do the payroll working alone ---NO GOOD!!!! the new computer can do the job in 1 hour less time and that would put us into negative time\r
\n" ); document.write( "\n" ); document.write( "CK
\n" ); document.write( "(1/6.55)+1/(5.55)=1/3
\n" ); document.write( "0.15267+0.18018=0.33333333
\n" ); document.write( "0.333~~~~~~0.333\r
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\n" ); document.write( "\n" ); document.write( "Hope this helps-----ptaylor\r
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