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2 parts
a

121.5 acres121.5 \text{ acres}

2160
b
195

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Part a· 5 steps

  1. Calculate the land allocated for medical buildings.

    The total land is 243 acres. Land for medical buildings is 0.5 of the total land.

    Land for medical buildings=0.5×243 acres=121.5 acres\text{Land for medical buildings} = 0.5 \times 243 \text{ acres} = \boxed{121.5 \text{ acres}}
  2. Calculate the remaining land and the land for planting grass.

    Remaining land after allocating for medical buildings:

    Remaining land=243 acres−121.5 acres=121.5 acres\text{Remaining land} = 243 \text{ acres} - 121.5 \text{ acres} = 121.5 \text{ acres}

    Land for planting grass is one-fifth of the remaining land:

    Land for planting grass=15×121.5 acres=24.3 acres\text{Land for planting grass} = \frac{1}{5} \times 121.5 \text{ acres} = 24.3 \text{ acres}
  3. Calculate the land allocated for staff quarters, waiting area, and parking area.

    This is the rest of the remaining land after allocating for grass planting.

    Land for SQ, WA, PA=121.5 acres−24.3 acres=97.2 acres\text{Land for SQ, WA, PA} = 121.5 \text{ acres} - 24.3 \text{ acres} = 97.2 \text{ acres}
  4. Determine the land specifically for the parking area.

    The ratios are Staff quarters (SQ) : Waiting area (WA) = 3 : 2 and Waiting area (WA) : Parking area (PA) = 1 : 2.
    To combine these ratios, we make the 'Waiting area' part common. Multiplying the second ratio by 2 gives WA : PA = 2:42 : 4.
    So, the combined ratio SQ : WA : PA = 3 : 2 : 4. The total number of ratio parts is 3+2+4=93 + 2 + 4 = 9.
    The parking area corresponds to 4 parts out of 9.

    Parking area=49×97.2 acres=4×97.29 acres=43.2 acres\text{Parking area} = \frac{4}{9} \times 97.2 \text{ acres} = \frac{4 \times 97.2}{9} \text{ acres} = 43.2 \text{ acres}
  5. Calculate the maximum number of cars that can occupy the parking area.

    One car occupies up to 0.02 acres.

    Maximum number of cars=43.2 acres0.02 acres/car=2160 cars\text{Maximum number of cars} = \frac{43.2 \text{ acres}}{0.02 \text{ acres/car}} = 2160 \text{ cars}

    Thus,

    Maximum number of cars=2160\text{Maximum number of cars} = \boxed{2160}

Part b195

  1. Determine the work rate of one man.

    Given: 2 men can clear 0.5 acres in 2 days.
    This means 1 man can clear 0.5 acres in 2×2=42 \times 2 = 4 days.

    Rate of 1 man=0.5 acres4 days=0.125 acres/day\text{Rate of 1 man} = \frac{0.5 \text{ acres}}{4 \text{ days}} = 0.125 \text{ acres/day}
  2. Calculate the total man-days required to clear 24.3 acres.

    Total man-days=24.3 acres0.125 acres/day/man=194.4 man-days\text{Total man-days} = \frac{24.3 \text{ acres}}{0.125 \text{ acres/day/man}} = 194.4 \text{ man-days}
  3. Determine the number of men needed to clear the land in 1 day.

    To complete the work in 1 day, the number of men required is equal to the total man-days. Since we cannot have a fraction of a man, we must round up to ensure the entire area is cleared.

    Number of men needed=⌈194.4⌉=195 men\text{Number of men needed} = \lceil 194.4 \rceil = 195 \text{ men}

    Thus,

    Number of men needed=195\text{Number of men needed} = \boxed{195}
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