Six machines at a certain factory operate at the same constant rate. if four of these machines, operating simultaneously, take 27 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?

18 hours

Explanation:

The key infomation here is that the machines operate at the same constant rate, so regardless of what the production is, all six machines would produce the same number of product per hour.

Lets set and easy example of the relationship:

The machines produce 1 product per hour, if 4 machines take 27 hours to fill the production order then: 4 × 27 × 1 = 108

The four machines takes 27 hours to produce the production order (which is 108 units)

So by simple rule of three we can know how much would take the six machines to produce the same amount by dividing the number of units produced by the number of machines taking in count that they produce at a rate of 1 unit per hour (the relationship stands even if you change the production rate):

Like we said before, the relationship is maintained whether the machines produce at a rate of 0,5 units per hour or 2 units per hour to say some examples, the result will always be the same (18 hours would take the six machines the produce the same production order).

you should think about the answers you give and expect the same form your questions.