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Calculate in km the distance cycled in Vineyard Race, Ocean to Ocean Race, and Karoo Fun Race.

Mathematics

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4 parts
4.1

112.65 km\text{112.65 km}

4.2

118.87 km\text{118.87 km}

4.3

270.80 km\text{270.80 km}

4.4

148.19 km\text{148.19 km}

Step-by-step solution

10 steps

Here are the solutions to Question 4.

Part 4.1· 2 steps

Calculate in km the distance cycled in Vineyard Race.

  1. Identify the distance given and the conversion factor.

    Distance = 70 miles70 \text{ miles}
    Conversion: 1 km=0.6214 miles1 \text{ km} = 0.6214 \text{ miles}

  2. Convert miles to kilometres.

    70 miles×1 km0.6214 miles=700.6214 km70 \text{ miles} \times \frac{1 \text{ km}}{0.6214 \text{ miles}} = \frac{70}{0.6214} \text{ km} 112.648857... km≈112.65 km112.648857... \text{ km} \approx 112.65 \text{ km}

    The distance cycled in Vineyard Race is 112.65 km\boxed{\text{112.65 km}}.

Part 4.2

118.87 km\text{118.87 km}

Calculate in km the distance cycled in Ocean to Ocean Race.

  1. Identify the distance given and the conversion factors.

    Distance = 130000 yards130 000 \text{ yards}
    Conversion: 1 yard=0.9144 metres1 \text{ yard} = 0.9144 \text{ metres} and 1 km=1000 metres1 \text{ km} = 1000 \text{ metres}

  2. Convert yards to metres, then metres to kilometres.

    130000 yards×0.9144 m1 yard×1 km1000 m130 000 \text{ yards} \times \frac{0.9144 \text{ m}}{1 \text{ yard}} \times \frac{1 \text{ km}}{1000 \text{ m}} =130000×0.91441000 km= \frac{130000 \times 0.9144}{1000} \text{ km} =130×0.9144 km= 130 \times 0.9144 \text{ km} =118.872 km≈118.87 km= 118.872 \text{ km} \approx 118.87 \text{ km}

    The distance cycled in Ocean to Ocean Race is 118.87 km\boxed{\text{118.87 km}}.

Part 4.3

270.80 km\text{270.80 km}

Calculate in km the distance cycled in Karoo Fun Race.

  1. Identify the distance given and the conversion factors.

    Distance = 888500 feet888 500 \text{ feet}
    Conversion: 1 m=3.281 feet1 \text{ m} = 3.281 \text{ feet} and 1 km=1000 metres1 \text{ km} = 1000 \text{ metres}

  2. Convert feet to metres, then metres to kilometres.

    888500 feet×1 m3.281 feet×1 km1000 m888 500 \text{ feet} \times \frac{1 \text{ m}}{3.281 \text{ feet}} \times \frac{1 \text{ km}}{1000 \text{ m}} =8885003.281×1000 km= \frac{888500}{3.281 \times 1000} \text{ km} =888.53.281 km= \frac{888.5}{3.281} \text{ km} =270.799756... km≈270.80 km= 270.799756... \text{ km} \approx 270.80 \text{ km}

    The distance cycled in Karoo Fun Race is 270.80 km\boxed{\text{270.80 km}}.

Part 4.4

148.19 km\text{148.19 km}

Calculate in km the distance cycled Charity Fun Sprint.

  1. Identify the distance given and the conversion factors.

    Distance = 5832154 inches5 832 154 \text{ inches}
    Conversion: 1 inch=2.54 cm1 \text{ inch} = 2.54 \text{ cm}, 1 m=100 cm1 \text{ m} = 100 \text{ cm}, and 1 km=1000 m1 \text{ km} = 1000 \text{ m}

  2. Convert inches to cm, cm to m, then m to km.

    5832154 inches×2.54 cm1 inch×1 m100 cm×1 km1000 m5 832 154 \text{ inches} \times \frac{2.54 \text{ cm}}{1 \text{ inch}} \times \frac{1 \text{ m}}{100 \text{ cm}} \times \frac{1 \text{ km}}{1000 \text{ m}} =5832154×2.54100×1000 km= \frac{5832154 \times 2.54}{100 \times 1000} \text{ km} =14818660.16100000 km= \frac{14818660.16}{100000} \text{ km} =148.1866016 km≈148.19 km= 148.1866016 \text{ km} \approx 148.19 \text{ km}

    The distance cycled in Charity Fun Sprint is 148.19 km\boxed{\text{148.19 km}}.

Part 4.5· 2 steps

Verify with calculations whether Jappie will be able to win the club cycling cup.

  1. Sum all the distances Jappie cycled (using more precise values before rounding).

    Total distance = Distance (Vineyard) + Distance (Ocean-to-Ocean) + Distance (Karoo) + Distance (Charity)

    Total distance=112.648857+118.872+270.799756+148.1866016 km\text{Total distance} = 112.648857 + 118.872 + 270.799756 + 148.1866016 \text{ km} Total distance=650.5072146 km\text{Total distance} = 650.5072146 \text{ km} Total distance≈650.51 km\text{Total distance} \approx 650.51 \text{ km}
  2. Compare the total distance to the required distance for the club cycling cup.

    Required distance = 600 km600 \text{ km}
    Since 650.51 km>600 km650.51 \text{ km} > 600 \text{ km}, Jappie has cycled more than the required distance.
    Therefore, Jappie will be able to win the club cycling cup.

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