Question 478492: As one alternative to gasoline-powered vehicles, flex fuel vehicles can use both regular gasoline and E85, a fuel containing 85% ethanol. The ethanol in E85 is derived from corn and other plants, a renewable resource, and burning E85 results in less pollution than gasoline. Because using E85 results in a lower fuel economy, its price per gallon must be lower than the price of gasoline in order to make it an economical fuel option. A 2007 Chevrolet Tahoe gets 21 mpg on the highway using gasoline and only 15 mpg on the highway using E85. If the price of gasoline is $3.36 a gallon, what must the price of E85 be in order for the fuel cost per mile to be the same?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! tahoe gets 21 mpg with gasoline and 15 mpg with ethanol.
cost for gas is $3.36.
cost for ethanol is x.
you want to know what the cost of ethanol should be to make gas and ethanol financially equivalent.
the formula that will help you find the equivalence is:
cpm = cpg / mpg
cpm = cost per mile
cpg = cost per gallon
mpg = miles per gallon
for gasoline, this formula would result in:
cpm = 3.36 / 21 = .16
for ethanol, this formula would result in:
cpm = cpg / 15
to get equivalence, you need to replace cpm with what we derived for gasoline.
the equation becomes:
.16 = cpg / 15
multiply both sides of this equation by 15 to get:
cpg = .16 * 15 which equals 2.4
the cost of ethanol per gallon needs to be 2.4 in order to make it financially equivalent to gasoline.
go back to your original equations:
for gasoline:
cpm = cpg / mpg = 3.36 / 21 = .16
for ethanol:
cpm = cpg / mpg = 2.4 / 15 = .16
gas and ethanol are comparable when the cost of ethanol is equal to $2.40 per gallon.
the formula was derived as follows:
m = number of miles
c = cost
mpg = miles per gallon
cpg = cost per gallon
m = g * mpg
this says that the number of miles you can travel is equal to the number of gallons you have * the miles per gallon.
c = g * cpg
this says that the total cost is equal to the number of gallons you bought times the cost per gallon.
if you want to get cost per mile (cpm) then you have to divide c by m to get:
cpm = c/m
since c = g*cpg and since m = g*mpg, you can substitute for c/m to get:
cpm = (g*cpg)/(g*mpg)
the g in the numerator and denominator cancels out and you are left with:
cpm = cpg/mpg
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