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Question 790028: Parallel processing uses two or more computers, working together, to solve a single problem. Using parallel processing, two computers can solve a problem in 6 minutes. If, working alone, one computer can solve a problem in 9 minutes less than the time needed by the second computer, how long would it take the faster computer working alone to solve the problem?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Let x = amount of time, in min the slower computer can do the task (on its own)
1/(x-9) + 1/x = 1/6
x/(x(x-9)) + (x-9)/(x(x-9)) = 1/6
(x + x-9)/(x(x-9)) = 1/6
(2x-9)/(x(x-9)) = 1/6
6(2x-9) = 1(x(x-9))
12x-54 = x^2-9x
0 = x^2-9x-12x+54
x^2-21x+54 = 0
(x-3)(x-18) = 0
x-3 = 0 or x-18 = 0
x = 3 or x = 18
Notice how if x = 3, then x-9 becomes 3-9 = -6. Since you can't have a negative time, this means that x = 3 is not allowed.
So x = 18 is the only allowed solution.
So it will take 18 minutes for the slower computer to do the job alone.
Therefore, it will take 18 - 9 = 9 minutes for the faster computer to do the job alone.
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