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10.1.1 Name the type of scale used on the map.

10.1.2 Explain the advantage of using this scale when the map is resized.

10.1.3 Thembi measured the distance from Vryheid to Durban on the map and found it to be 77 mm. Use the scale to find the actual distance, in kilometers, rounded off to one decimal place, that Thembi will travel. (2)

10.1.4 Thembi intends to leave Vryheid at 7:30. If she travels at an average speed of 108 km/h, considering traffic delays, calculate at what time she will reach Durban. You may use the equation: Speed = distance ÷ time. (4)

10.1.5 Thembi's car consumes 6.2 liters of fuel per 100 km. Calculate how many liters of fuel Thembi's car will consume for the return trip. (3)

10.1.6 Thembi concluded that R2,600 will be enough to pay for the return trip, including fuel, accommodation, and toll gates. Toll gates cost R49 for a single trip. Verify if her calculations are correct. (10)​

Answer :

10.1.1 Type of Scale: The scale provided in the question appears to be a representative fraction or ratio scale, often written as 1:80 (where "MLS 80" suggests a scale of 1:80).

10.1.2 Advantage of Using This Scale: The advantage of using a representative fraction scale is that it remains accurate regardless of how the map is resized. Whether you enlarge or reduce the map, the ratio between distances on the map and actual ground distances remains the same.

10.1.3 Calculating the Actual Distance:

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[tex]\text{If the map scale is 1:80, it means 1 unit on the map represents 80 units on the ground.}[/tex]

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[tex]\text{Thembi measures 77 mm on the map. Thus, the actual distance is:}[/tex]

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[tex]\text{Actual Distance} = 77 \text{ mm} \times 80 = 6160 \text{ mm}.[/tex]

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[tex]\text{Converting mm to km: 6160 \text{ m} = 6.160 \text{ km}.
\text{Rounding: 6.2 \text{ km}[/tex]

10.1.4 Estimating Arrival Time:

  • Thembi's average speed: 108 km/h.

  • [tex]\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{6.2}{108} \approx 0.0575 \text{ hours}.[/tex]

  • 0.0575 hours [tex]\approx[/tex] 3.45 minutes.

  • If Thembi leaves at 7:30, she will arrive at approximately 7:33.

10.1.5 Fuel Consumption for the Round Trip:

  • Fuel consumption rate: 6.2 liters per 100 km.

  • Total distance for the round trip is 12.4 km (6.2 km one way).

  • [tex]\text{Fuel needed for round trip} = (12.4 \times 6.2) \div 100 \approx 0.77 \text{ liters.[/tex]

10.1.6 Cost Verification for the Trip:

  1. Fuel Cost:

    • Assume fuel cost is [tex]R[/tex] Liters: using [tex]R \approx 0.77 \text{ liters}[/tex].
    • If 1 liter cost, e.g., R20: Fuel cost = 0.77 [tex]\times[/tex] R20 [tex]\approx R \text{62}[/tex].

  2. Toll Gates:

    • Single trip: R49.
    • Total (round trip): R49 [tex]\times 2 = R98[/tex].

  3. Accommodation and Other Costs: Subtract the total fuel and toll costs from R2,600 to determine the remaining budget:

    -
    [tex]\text{Remaining Budget} = R2,600 - (R62 + R98) \approx R2,440[/tex]

    • As she plans to budget for accommodation and other costs with the remaining amount (R2,440), she should have enough to cover all.

Hence, calculating these costs, Thembi's budget seems sufficient for the trip, if accommodation and other expenses do not surpass R2,440.

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