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A farmer has 6 tractors, each ploughing 120 hectares a day. They complete a field in 4 days. If 2 tractors are removed, how many days will it take the remaining tractors to finish the field? What is t

Mathematics

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Answer

144 HECTARES\text{144 HECTARES}

Step-by-step solution

4 steps
  1. Calculate the total area of the field.

    Initially, there are 6 tractors, and each ploughs 120 hectares a day. They complete the field in 4 days.
    Total hectares ploughed per day by 6 tractors:

    6 tractors×120hectarestractor⋅day=720hectaresday6 \text{ tractors} \times 120 \frac{\text{hectares}}{\text{tractor} \cdot \text{day}} = 720 \frac{\text{hectares}}{\text{day}}

    Total area of the field:

    720hectaresday×4 days=2880 hectares720 \frac{\text{hectares}}{\text{day}} \times 4 \text{ days} = 2880 \text{ hectares}
  2. Determine the number of remaining tractors.

    Two tractors were moved, so the remaining tractors are:

    6−2=4 tractors6 - 2 = 4 \text{ tractors}
  3. Calculate the total hectares ploughed per day by the remaining tractors.

    The remaining 4 tractors plough the same 2880-hectare field in 5 days.
    Total hectares ploughed per day by 4 tractors:

    2880 hectares5 days=576hectaresday\frac{2880 \text{ hectares}}{5 \text{ days}} = 576 \frac{\text{hectares}}{\text{day}}
  4. Calculate how many hectares one tractor would plough a day.

    Divide the total hectares ploughed per day by the number of remaining tractors:

    576hectaresday4 tractors=144hectarestractor⋅day\frac{576 \frac{\text{hectares}}{\text{day}}}{4 \text{ tractors}} = 144 \frac{\text{hectares}}{\text{tractor} \cdot \text{day}}

    One tractor would plough 144 hectares a day.

    The final answer is 144 HECTARES\text{144 HECTARES}.

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