Machine M can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
For combined rates problems, if you can work out what each machine does in the same amount of time
, the problem will almost always become easy. Since x is unimportant here, rather than talk about 'producing x units', I'll simply talk about 'completing one job'. Say it takes M t hours to complete one job. Then we know, from the ratios provided:
M completes one job in t hours
N completes one job in 4t/3 hours
O completes one job in 2t hours
We can easily work out what each would do in 4t hours:
M completes 4 jobs in 4t hours
N completes 3 jobs in 4t hours
O completes 2 jobs in 4t hours
So if they work together for the same amount of time, M does 4/9 of the work, N does 3/9 = 1/3 of the work, and O does 2/9 of the work. The answer is 1/3.
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