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How many people will be needed to erect the fence in 4 days? 2.2. If one person rates R70/hour. How much will be the total cost of labourers in 3 days if 3 people work for 8 hours a day?

Mathematics

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2 parts
2.1

28 people\text{28 people}

2.2

R5040\text{R}5040

Step-by-step solution

5 steps

Here are the solutions for Activity 2.

Part 2.1· 2 steps

  1. Determine the total work units.

    The work required to erect the fence is constant. It is calculated as the number of people multiplied by the number of days.

    Total work=People×Days\text{Total work} = \text{People} \times \text{Days} Total work=14 people×8 days\text{Total work} = 14\, \text{people} \times 8\, \text{days} Total work=112 person-days\text{Total work} = 112\, \text{person-days}
  2. Calculate the number of people needed for the new timeframe.

    To complete the same amount of work in 4 days, we divide the total work by the new number of days.

    Number of people=Total workNew number of days\text{Number of people} = \frac{\text{Total work}}{\text{New number of days}} Number of people=112 person-days4 days\text{Number of people} = \frac{112\, \text{person-days}}{4\, \text{days}} Number of people=28 people\text{Number of people} = 28\, \text{people}

    To erect the fence in 4 days, 28 people will be needed.

    28 people\boxed{\text{28 people}}

Part 2.2

R5040\text{R}5040

  1. Calculate the total hours worked by one person.

    One person works for 8 hours a day for 3 days.

    Hours per person=8 hours/day×3 days\text{Hours per person} = 8\, \text{hours/day} \times 3\, \text{days} Hours per person=24 hours\text{Hours per person} = 24\, \text{hours}
  2. Calculate the total hours worked by all labourers.

    There are 3 people working.

    Total hours worked=Hours per person×Number of people\text{Total hours worked} = \text{Hours per person} \times \text{Number of people} Total hours worked=24 hours×3\text{Total hours worked} = 24\, \text{hours} \times 3 Total hours worked=72 hours\text{Total hours worked} = 72\, \text{hours}
  3. Calculate the total cost.

    Each person rates R70 per hour.

    Total cost=Total hours worked×Rate per hour\text{Total cost} = \text{Total hours worked} \times \text{Rate per hour} Total cost=72 hours×R70/hour\text{Total cost} = 72\, \text{hours} \times \text{R}70/\text{hour} Total cost=R5040\text{Total cost} = \text{R}5040

    The total cost of labourers will be R5040.

    R5040\boxed{\text{R}5040}
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