Question 816829: [ If one car costs $14,300 and it gets 35 mpg. And the other car costs [$15,400] and gets 40 mpg. Assuming that gas costs $3.75 per gallon [at what number of driven miles] would the two cars [be of equal value?] ]
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! 3.75 $/gallon
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x = miles driven
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car a:
m = 3.75 $/gal * (1/35) gal/mile = 0.1071428 $/mile (fuel cost per mile)
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car b:
m = 3.75 $/gal * (1/40) gal/mile = 0.09375 $/mile (fuel cost per mile)
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cost of ownership per mile:
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a(x) = 0.1071428x + 14300
b(x) = 0.09375x + 15400
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break even point:
0.1071428x + 14300 = 0.09375x + 15400
0.1071428x - 0.09375x = 15400 - 14300
0.0133928x = 1100
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x = 82134 miles
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Answer:
the more fuel efficient car-a, which is $1100 more expensive to purchase, will not match the less fuel efficient car-b in terms of operating cost per mile, until the cars have each been driven 82,134 miles. In other words, the more fuel efficient car-a will cost more to operate per mile than car-b, until both cars have each been driven 82,134 miles, at which time car-a will cost less to operate per mile than car-b.
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