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Difficulty: EasyWork Rate and Combined Work

Printer Alpha can fabricate a set of architectural prototypes in 44 hours operating alone at a constant rate. Printer Beta can fabricate the exact same set of prototypes in 1212 hours operating alone at a constant rate. If both printers operate simultaneously at their respective constant rates, how many hours will it take them to fabricate one set of architectural prototypes?

  1. A
    1616 hours
  2. B
    88 hours
  3. 33 hoursAnswer
  4. D
    66 hours
  5. E
    4.84.8 hours

Answer

33 hours
The correct answer is 33 hours. The rate of Printer Alpha is 14\frac{1}{4} of the prototype set per hour, and the rate of Printer Beta is 112\frac{1}{12} of the set per hour. Their combined rate when operating simultaneously is 14+112=412=13\frac{1}{4} + \frac{1}{12} = \frac{4}{12} = \frac{1}{3} set per hour. Therefore, the time required to complete 11 set working together is 113=3\frac{1}{\frac{1}{3}} = 3 hours.

Step-by-Step Solution

1
Determine the individual work rate for Printer Alpha.
Printer Alpha completes 14\frac{1}{4} of the job per hour.
Work rate is defined as job completed divided by time taken.
2
Determine the individual work rate for Printer Beta.
Printer Beta completes 112\frac{1}{12} of the job per hour.
Work rate is defined as job completed divided by time taken.
3
Add the individual rates to find the combined work rate.
Combined rate = 14+112=312+112=412=13\frac{1}{4} + \frac{1}{12} = \frac{3}{12} + \frac{1}{12} = \frac{4}{12} = \frac{1}{3} of the job per hour.
When entities work together, their individual rates add up.
4
Calculate the total time required for the combined rate to complete 1 job.
Time = 1Combined Rate=113=3\frac{1}{\text{Combined Rate}} = \frac{1}{\frac{1}{3}} = 3 hours.
Time is the reciprocal of the combined rate.

Key Concept

Combined Work Rate
Estimated Time:45s
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Topics

Work Rate and Combined Work

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