It takes two hours for two machines to manufacture 10000 parts. If machine #1 can do the job in one hour less than machine #2, how long does it take for each machine to manufacture 10000 parts alone
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.
1/x + 1/(x-1) = 1/2
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.
Does this help?