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Zorluk: OrtaRatio, Proportion, and Rate

A team of 88 identical excavators working together at a constant rate can clear a parcel of land in 15 days15\text{ days}. All 88 excavators work together for the first 3 days3\text{ days}, after which 22 excavators break down and are removed from the site. Assuming the remaining excavators continue working at the same constant rate, how many additional days will it take to complete the clearing of the land?

  1. 16 days16\text{ days}Cevap
  2. B
    20 days20\text{ days}
  3. C
    12 days12\text{ days}
  4. D
    13 days13\text{ days}

Cevap

The correct answer is 16 days16\text{ days}.
The total work required for the project is 120120 excavator-days. During the first 33 days, the 88 excavators complete 2424 excavator-days of work, leaving 9696 excavator-days of work remaining. Since 22 excavators break down, 66 excavators remain. The additional time needed for these 66 excavators to clear the rest of the land is 96÷6=1696 \div 6 = 16 days.

Adım Adım Çözüm

1
Calculate the total work required in excavator-days.
Total Work=8 excavators×15 days=120 excavator-days\text{Total Work} = 8 \text{ excavators} \times 15 \text{ days} = 120 \text{ excavator-days}.
Work done is directly proportional to the product of rate (number of machines) and time.
2
Calculate the work completed in the first 3 days and the remaining work.
Work Done=8×3=24 excavator-days\text{Work Done} = 8 \times 3 = 24 \text{ excavator-days}; Remaining Work=120−24=96 excavator-days\text{Remaining Work} = 120 - 24 = 96 \text{ excavator-days}.
Subtracting completed work from total work yields the portion left to be done.
3
Determine the number of remaining excavators and compute the additional days required.
Remaining Excavators=8−2=6\text{Remaining Excavators} = 8 - 2 = 6; Additional Days=96 excavator-days6 excavators=16 days\text{Additional Days} = \frac{96 \text{ excavator-days}}{6 \text{ excavators}} = 16 \text{ days}.
Dividing the remaining work by the active rate gives the time needed to finish the project.

Anahtar Kavram

Inverse proportion and work-rate problem involving partial completion and workforce changes.
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Konular

Ratio, Proportion, and Rate

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