To find out when upgrading the car becomes a better choice, we’ll calculate the annual fuel cost for both the current and upgraded truck, then compare it to the annual fuel cost for the upgraded car.
Current annual fuel cost for the truck:
12,000 miles / 10 mpg * $2.65/gallon = $3,180
Upgraded annual fuel cost for the truck:
12,000 miles / 12.5 mpg * $2.65/gallon = $2,136
Annual fuel cost for the upgraded car:
12,000 miles / 40 mpg * $2.65/gallon = $792
Now, we’ll compare the upgraded car’s annual fuel cost to the upgraded truck’s annual fuel cost:
$792 < $2,136
So, upgrading the car becomes the better choice once the annual mileage driven exceeds $2,136 - $792 = $1,344.
To find out how many miles you would need to drive the car for this to be true:
$1,344 / ($2.65/gallon * (1/25 - 1/40)) = 36,582 miles
Therefore, you would need to drive the car for approximately 36,582 miles before upgrading it becomes the better choice.
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