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Zorluk: ZorRatios, Rates, and Proportions

A construction crew of 1212 workers can build 22 identical storage sheds in 88 days, working 66 hours per day. To complete a new project of building 33 of these same storage sheds in 66 days, how many additional workers, working at the same rate, must be hired if they will work 44 hours per day?

  1. A
    4
  2. B
    12
  3. C
    16
  4. 24Cevap
  5. E
    36

Cevap

The correct answer is 24 additional workers.
The correct answer is 24 additional workers. First, calculate the rate of work: 1212 workers working 66 hours per day for 88 days is 12×8×6=57612 \times 8 \times 6 = 576 total worker-hours to complete 22 sheds, which equals 288288 worker-hours per shed. For the new project of 33 sheds, the total worker-hours needed is 3×288=8643 \times 288 = 864 hours. Under the new schedule of 66 days at 44 hours per day, each worker will work 6×4=246 \times 4 = 24 hours. Thus, the total number of workers required is 864/24=36864 / 24 = 36 workers. Subtracting the original crew of 1212 workers, the crew needs to hire 36−12=2436 - 12 = 24 additional workers.

Adım Adım Çözüm

1
Calculate the total worker-hours required to build one storage shed.
288 worker-hours per shed
A crew of 1212 workers working for 88 days at 66 hours per day contributes a total of 12×8×6=57612 \times 8 \times 6 = 576 worker-hours to build 22 sheds. Dividing 576576 by 22 gives 288288 worker-hours per shed.
2
Determine the total worker-hours required for the new project of building 3 sheds.
864 worker-hours
Since each shed requires 288288 worker-hours, building 33 sheds will require 3×288=8643 \times 288 = 864 worker-hours.
3
Calculate the number of hours each worker will contribute under the new schedule.
24 hours per worker
On the new schedule, workers work for 66 days at 44 hours per day, which equals 6×4=246 \times 4 = 24 hours per worker.
4
Calculate the total number of workers required and the number of additional workers to hire.
36 total workers, which means 24 additional workers
Dividing the total required hours (864864) by the hours per worker (2424) gives 3636 total workers. Subtracting the initial crew of 1212 workers yields 36−12=2436 - 12 = 24 additional workers.

Anahtar Kavram

Compound rates and proportional relationships

Alternatif Yöntem

We can set up a compound proportion equation where W1⋅D1⋅H1S1=W2⋅D2⋅H2S2\frac{W_1 \cdot D_1 \cdot H_1}{S_1} = \frac{W_2 \cdot D_2 \cdot H_2}{S_2}. Substituting the known values: 12⋅8⋅62=W2⋅6⋅43\frac{12 \cdot 8 \cdot 6}{2} = \frac{W_2 \cdot 6 \cdot 4}{3}. Simplifying both sides gives 288=8W2288 = 8 W_2, which yields W2=36W_2 = 36. The number of additional workers is 36−12=2436 - 12 = 24.
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