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Problem-Solving and Data AnalysisMediumDensity / rate as a unit rate

Problem-Solving and Data Analysis practice question

A machine fills 3 bottles every 4 seconds. How many seconds does it take to fill 27 bottles?

Answer: 36

The rate is 3 bottles per 4 seconds, so 27 bottles is 27/3 = 9 groups of 3, each taking 4 seconds: 9 × 4 = 36 seconds. The trap is multiplying 27 × 4 = 108 without accounting for the 3 bottles filled per interval.

Common wrong answers

If you answered 9
You correctly found 9 groups of 3 bottles, but stopped there — each group takes 4 seconds, so multiply: 9 × 4 = 36.
If you answered 108
You multiplied 27 × 4, treating 4 seconds as the time for one bottle — but 4 seconds fills 3 bottles, so you need 27 ÷ 3 = 9 intervals of 4 seconds.
If you answered 6.75
You divided 27 by 4, but 4 is the seconds per group, not the bottles per group; divide by 3 to get 9 intervals, then multiply by 4.

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