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Difficulty: EasyWork Rate and Combined Work

Technician A can assemble a solar panel frame in 66 hours working alone at a constant rate. Technician B can assemble the exact same solar panel frame in 33 hours working alone at a constant rate. Working together at their respective constant rates, how many hours will it take Technician A and Technician B to assemble one solar panel frame?

  1. A
    1.51.5 hours
  2. 22 hoursAnswer
  3. C
    33 hours
  4. D
    4.54.5 hours
  5. E
    99 hours

Answer

Working together, Technician A and Technician B will complete the assembly in 22 hours.
The correct option is 22 hours because Technician A completes 16\frac{1}{6} of the work in one hour and Technician B completes 13\frac{1}{3} (or 26\frac{2}{6}) of the work in one hour. Combined, they complete 36=12\frac{3}{6} = \frac{1}{2} of the work each hour, so the entire job takes 22 hours.

Step-by-Step Solution

1
Determine individual work rates per hour.
Technician A's rate is 16\frac{1}{6} frame per hour, and Technician B's rate is 13\frac{1}{3} frame per hour.
Work rate is defined as the fraction of a job completed per unit of time, calculated as 1time\frac{1}{\text{time}}.
2
Add the individual rates to find the combined rate.
Combined rate =16+13=16+26=36=12= \frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2} frame per hour.
When entities work simultaneously, their individual rates add up.
3
Calculate total time required for one full frame.
Total time =1Combined Rate=11/2=2= \frac{1}{\text{Combined Rate}} = \frac{1}{1/2} = 2 hours.
Total time required is the reciprocal of the combined work rate.

Key Concept

Combined Work Rate Formula
Estimated Time:50s
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Topics

Work Rate and Combined Work

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