The vehicles covered a trip of 200,000 km during the month. Estimated annual expenses were as follows: Repairs 46,800, Tyre-Tube expenses 36,000, Licence, Insurance etc 37,500, Ren... The vehicles covered a trip of 200,000 km during the month. Estimated annual expenses were as follows: Repairs 46,800, Tyre-Tube expenses 36,000, Licence, Insurance etc 37,500, Rent & Rates of the Garage 22,750, Miscellaneous expenses 75,000. What is the total operating cost per mile?
Understand the Problem
The question relates to estimating annual expenses based on a journey of 200,000 kilometers. It lists various expenses such as repairs, tyre-tube expenses, licenses, insurance, rent for the garage, and miscellaneous costs, and asks to calculate the total operating cost per mile based on these figures.
Answer
The total operating cost per mile is approximately $2.42$.
Answer for screen readers
The total operating cost per mile is approximately (C \approx 2.42).
Steps to Solve
- Calculate Total Annual Expenses
Add all the annual expenses together:
- Repairs: 46,800
- Tyre-Tube expenses: 36,000
- Licence, Insurance, etc.: 37,500
- Rent & Rates of the Garage: 22,750
- Miscellaneous expenses: 75,000
The total annual expenses ((E)) can be calculated as:
$$ E = 46800 + 36000 + 37500 + 22750 + 75000 $$
- Calculate the Total Operating Cost
Sum all the values calculated in the previous step:
$$ E = E = 46800 + 36000 + 37500 + 22750 + 75000 = 221050 $$
- Convert Kilometers to Miles
Since the operating cost is required per mile, convert the distance from kilometers to miles. There are approximately 0.621371 miles in a kilometer:
$$ \text{Distance in miles} = 200000 \times 0.621371 $$
- Calculate the Operating Cost per Mile
Divide the total annual expenses by the total distance in miles to find the operating cost per mile ((C)):
$$ C = \frac{E}{\text{Distance in miles}} $$
Plug in the values calculated:
$$ C = \frac{221050}{200000 \times 0.621371} $$
- Final Calculation
Perform the calculations to finalize the result for (C).
The total operating cost per mile is approximately (C \approx 2.42).
More Information
The operating costs per mile give insight into the financial efficiency of running the vehicle. Knowing these costs can assist in budgeting for future journeys and managing expenses effectively.
Tips
- Forgetting to convert kilometers to miles before calculating the cost per mile.
- Miscalculating the total annual expenses by omitting one of the components.
- Using incorrect conversion factors between kilometers and miles.
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