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Lili budgeted R6000.00, for fuel, toll gates, gift and accommodation for two nights. Determine showing all calculations whether the Lili's budget will be sufficient.

Mathematics

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2 parts
40.8

13:15\text{13:15}

40.9

sufficient\text{sufficient}

Step-by-step solution

13 steps

Part 40.4

This question requires information from a map that was not provided. Therefore, I cannot identify the last town.

Part 40.5

This question requires information from a map that was not provided. Therefore, I cannot identify any regional roads.

Part 40.6

This question requires information from a map that was not provided. Therefore, I cannot identify the national park.

Part 40.7· 2 steps

Lili stated that it would take her just 7 hours only to reach Port Elizabeth if she travelled at an average speed of 115 km per hour. Verify with calculations if she is correct.

  1. Calculate the distance Lili would cover.

    The formula for distance is Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}.

    Distance=115 km/h×7 h\text{Distance} = 115 \text{ km/h} \times 7 \text{ h} Distance=805 km\text{Distance} = 805 \text{ km}

  2. Verify Lili's statement.

    Lili would cover 805 km805 \text{ km} in 7 hours at an average speed of 115 km/h115 \text{ km/h}. To verify if her statement is correct, the actual distance from her starting point to Port Elizabeth would be needed. Since this actual distance is not provided, we cannot definitively verify if her statement is correct. If the actual distance is 805 km805 \text{ km}, then her statement is correct.

Part 40.8

13:15\text{13:15}

Lili intends to leave Durban at 05:30 and makes 3 stops which will be 15 min each. Calculate what time she will reach her destination.

  1. Determine the total driving time.

    Based on Lili's statement in 40.7, we assume the driving time is 7 hours.

  2. Calculate the total time spent on stops.

    Lili makes 3 stops, each 15 minutes long.

    Total stop time=3×15 minutes\text{Total stop time} = 3 \times 15 \text{ minutes} Total stop time=45 minutes\text{Total stop time} = 45 \text{ minutes}

  3. Calculate the total duration of the trip.

    Total trip duration=Driving time+Total stop time\text{Total trip duration} = \text{Driving time} + \text{Total stop time} Total trip duration=7 hours+45 minutes\text{Total trip duration} = 7 \text{ hours} + 45 \text{ minutes} Total trip duration=7 hours and 45 minutes\text{Total trip duration} = 7 \text{ hours and } 45 \text{ minutes}

  4. Calculate the arrival time.

    Lili leaves Durban at 05:30.

    Arrival time=05:30+7 hours 45 minutes\text{Arrival time} = 05:30 + 7 \text{ hours } 45 \text{ minutes} Arrival time=12:75\text{Arrival time} = 12:75

    Since 75 minutes is 1 hour and 15 minutes:

    Arrival time=12:00+1 hour 15 minutes\text{Arrival time} = 12:00 + 1 \text{ hour } 15 \text{ minutes} Arrival time=13:15\text{Arrival time} = 13:15

    Lili will reach her destination at 13:15\boxed{\text{13:15}}.

Part 40.9

sufficient\text{sufficient}

Lili budgeted R6000.00, for fuel, toll gates, gift and accommodation for two nights. Determine showing all calculations whether the Lili's budget will be sufficient.

  1. Calculate the total distance for the return trip.

    From 40.7, the one-way distance is 805 km805 \text{ km}. Assuming a return trip for fuel based on the "toll gates (return)" information:

    Total distance=805 km×2\text{Total distance} = 805 \text{ km} \times 2 Total distance=1610 km\text{Total distance} = 1610 \text{ km}

  2. Calculate the total fuel needed.

    Fuel consumption is 7.5 L7.5 \text{ L} per 100 km100 \text{ km}.

    Fuel needed=1610 km100 km×7.5 L\text{Fuel needed} = \frac{1610 \text{ km}}{100 \text{ km}} \times 7.5 \text{ L} Fuel needed=16.1×7.5 L\text{Fuel needed} = 16.1 \times 7.5 \text{ L} Fuel needed=120.75 L\text{Fuel needed} = 120.75 \text{ L}

  3. Calculate the total fuel cost.

    Fuel cost is R23.20 per litre.

    Fuel cost=120.75 L×R23.20/L\text{Fuel cost} = 120.75 \text{ L} \times \text{R}23.20/\text{L} Fuel cost=R2799.40\text{Fuel cost} = \text{R}2799.40

  4. Calculate the accommodation cost.

    Accommodation is R950 per person per day for two nights. Assuming Lili is traveling alone:

    Accommodation cost=R950/day×2 nights\text{Accommodation cost} = \text{R}950/\text{day} \times 2 \text{ nights} Accommodation cost=R1900.00\text{Accommodation cost} = \text{R}1900.00

  5. List other costs.

    Toll gates (return): R300.00
    Gift: R500.00

  6. Calculate the total expenses.

    Total expenses=Fuel cost+Accommodation cost+Toll gates+Gift\text{Total expenses} = \text{Fuel cost} + \text{Accommodation cost} + \text{Toll gates} + \text{Gift} Total expenses=R2799.40+R1900.00+R300.00+R500.00\text{Total expenses} = \text{R}2799.40 + \text{R}1900.00 + \text{R}300.00 + \text{R}500.00 Total expenses=R5499.40\text{Total expenses} = \text{R}5499.40

  7. Compare total expenses with the budget.

    Lili's budget is R6000.00.
    Since R5499.40 is less than R6000.00, Lili's budget is sufficient.

    Remaining budget=R6000.00−R5499.40\text{Remaining budget} = \text{R}6000.00 - \text{R}5499.40 Remaining budget=R500.60\text{Remaining budget} = \text{R}500.60

    Lili's budget will be sufficient\boxed{\text{sufficient}}.

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