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3 parts
a

25 km2\text{25 } km^2

b

2 hours, 18 minutes and 28 seconds\text{2 hours, 18 minutes and 28 seconds}

c

UGX 13,714,286\text{UGX 13,714,286}

Step-by-step solution

11 steps

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Part a· 2 steps

Real area of the piece of land in km2km^2

  1. Convert the map scale from cmcm to kmkm.

    The map scale is 1:250,0001:250,000, meaning 1 cm1 \, cm on the map represents 250,000 cm250,000 \, cm on the ground.
    We know that 100 cm=1 m100 \, cm = 1 \, m and 1000 m=1 km1000 \, m = 1 \, km.
    So, 250,000 cm=250,000100 m=2,500 m250,000 \, cm = \frac{250,000}{100} \, m = 2,500 \, m.
    And 2,500 m=2,5001000 km=2.5 km2,500 \, m = \frac{2,500}{1000} \, km = 2.5 \, km.
    Therefore, 1 cm1 \, cm on the map represents 2.5 km2.5 \, km on the ground.

  2. Calculate the real area.

    For area, we square the linear scale.
    1 cm21 \, cm^2 on the map represents (2.5 km)2(2.5 \, km)^2 on the ground.

    (2.5 km)2=6.25 km2(2.5 \, km)^2 = 6.25 \, km^2

    The area on the map is 4 cm24 \, cm^2.
    Real area = Area on map ×\times (Area scale factor)

    Real area=4 cm2×6.25 km2cm2=25 km2\text{Real area} = 4 \, cm^2 \times 6.25 \, \frac{km^2}{cm^2} = 25 \, km^2

    The real area of the piece of land is 25 km2\boxed{\text{25 } km^2}.

Part b

2 hours, 18 minutes and 28 seconds\text{2 hours, 18 minutes and 28 seconds}

Time taken by the tractors to plough 10 acres

  1. Find the individual ploughing rates for each tractor.

    Tractor A ploughs 1 acre in 45 minutes. Rate of A (RAR_A) = 1 acre45 minutes\frac{1 \, \text{acre}}{45 \, \text{minutes}}.
    Tractor B ploughs 1 acre in 20 minutes. Rate of B (RBR_B) = 1 acre20 minutes\frac{1 \, \text{acre}}{20 \, \text{minutes}}.

  2. Find the combined ploughing rate when both tractors work together.

    Combined rate (RtotalR_{total}) = RA+RBR_A + R_B

    Rtotal=145+120 acres/minuteR_{total} = \frac{1}{45} + \frac{1}{20} \, \text{acres/minute}

    To add these fractions, find the least common multiple (LCM) of 45 and 20, which is 180.

    Rtotal=1×445×4+1×920×9=4180+9180=13180 acres/minuteR_{total} = \frac{1 \times 4}{45 \times 4} + \frac{1 \times 9}{20 \times 9} = \frac{4}{180} + \frac{9}{180} = \frac{13}{180} \, \text{acres/minute}

  3. Calculate the time required to plough 10 acres.

    Time = Total areaCombined rate\frac{\text{Total area}}{\text{Combined rate}}

    Time=10 acres13180 acres/minute=10×18013 minutes=180013 minutes\text{Time} = \frac{10 \, \text{acres}}{\frac{13}{180} \, \text{acres/minute}} = 10 \times \frac{180}{13} \, \text{minutes} = \frac{1800}{13} \, \text{minutes}

  4. Convert the time to hours and minutes.

    180013 minutes≈138.4615 minutes\frac{1800}{13} \, \text{minutes} \approx 138.4615 \, \text{minutes}

    138 minutes is equal to 2 hours and 18 minutes (138=2×60+18138 = 2 \times 60 + 18).
    The remaining fraction of a minute is 0.4615×60≈27.690.4615 \times 60 \approx 27.69 seconds.

    The time taken by the tractors to plough 10 acres is approximately 2 hours, 18 minutes and 28 seconds\boxed{\text{2 hours, 18 minutes and 28 seconds}}.

Part c

UGX 13,714,286\text{UGX 13,714,286}

Find the total budget for ploughing

  1. Express the contributions as fractions of the total budget.

    Let the total budget be BB.
    Clergy's contribution = 25B\frac{2}{5} B.
    MP's contribution = 14B\frac{1}{4} B.

  2. Calculate the fraction of the budget remaining after the Clergy's and MP's contributions.

    Total contributions from Clergy and MP = 25B+14B=(820+520)B=1320B\frac{2}{5} B + \frac{1}{4} B = \left(\frac{8}{20} + \frac{5}{20}\right) B = \frac{13}{20} B.
    Remaining fraction = B−1320B=720BB - \frac{13}{20} B = \frac{7}{20} B.

  3. Calculate the fraction contributed by the group members.

    The group members contributed half of the remaining fraction.
    Group members' contribution = 12×720B=740B\frac{1}{2} \times \frac{7}{20} B = \frac{7}{40} B.

  4. Calculate the total monetary contribution from the group members.

    There are 48 group members, and each contributed UGX 50,000.
    Total contribution from group members = 48×50,000 UGX=2,400,000 UGX48 \times 50,000 \, \text{UGX} = 2,400,000 \, \text{UGX}.

  5. Equate the group members' contribution (as a fraction and in money) to find the total budget.

    740B=2,400,000 UGX\frac{7}{40} B = 2,400,000 \, \text{UGX} B=2,400,000×407 UGXB = 2,400,000 \times \frac{40}{7} \, \text{UGX} B=96,000,0007 UGXB = \frac{96,000,000}{7} \, \text{UGX} B≈13,714,285.71 UGXB \approx 13,714,285.71 \, \text{UGX}

    Rounding to the nearest shilling.

    The total budget for ploughing is approximately UGX 13,714,286\boxed{\text{UGX 13,714,286}}.

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