SOLUTION: 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

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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?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes the old computer working alone to do the payroll
Then the old computer works at the rate of 1/x of the payroll per hour
We are told that the new computer working alone can do the payroll in x-1 hours
Then the new computer works at the rate of 1/(x-1) of the payroll per hour
Together the two computers work at the rate of 1/x + 1/(x-1) of the payroll per hour
We are also told that when both computers are used, they can do the job in 3 hours.
So, together the computers work at the rate of 1/3 of the payroll per hour
So, our equation to solve is:
1/x + 1/(x-1)=1/3 multiply each term by 3*x*(x-1)
3(x-1)+3x=x(x-1) simplify
3x-3+3x=x^2-x or
6x-3=x^2-x subtract 6x from and add 3 to both sides
6x-6x-3+3=x^2-x-6x+3 collect like terms
x^2-7x+3=0-----------Quadratic in standard form; solve using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%287%2B-+sqrt%28+49-12+%29%29%2F%282%29+
x+=+%287%2B-+sqrt%2837%29%29%2F%282%29+
x+=+%287%2B-6.1%29%2F%282%29+
x+=+%287%2B6.1%29%2F%282%29+
x+=+6.55hr+------------------time it takes the old computer to do the payroll working alone
x-1=6.55-1=5.55hr+-----time it would take the new computer working alone
Another possible solution is:
x+=+%287-6.1%29%2F%282%29+
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
CK
(1/6.55)+1/(5.55)=1/3
0.15267+0.18018=0.33333333
0.333~~~~~~0.333

Hope this helps-----ptaylor