SOLUTION: It takes two hours for two machines to manufacture 10,000 parts. If Machine #1 can do the job alone in one hour less than Machine #2 can do the job, how long does it take for each

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Question 1117563: It takes two hours for two machines to manufacture 10,000 parts. If Machine #1 can do the job alone in one hour less than Machine #2 can do the job, how long does it take for each machine to manufacture10,000 parts alone?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Use the standard method for solving "working together" problems: make an equation showing the fractions of the job that each worker does in a fixed amount of time.

Let x be the number of hours required by the slower machine; then x-1 is the number of hours required by the faster machine.

Then the fractions of the job each does in 1 hour are 1/x and 1/x-1.

And the fraction of the job they do together in 1 hour is 1/2.

So

1%2Fx+%2B+1%2F%28x-1%29+=+1%2F2

Multiply both sides of the equation by the least common denominator to clear fractions. You will end up with a quadratic equation that does not factor; so you will need to get your irrational answer using the quadratic formula or something like a graphing calculator.