The Mathematics of Hybrid Cars
This week I found an article on CNN's web page entitled "Hybrids: Don't Buy the Hype". Note that this link may become invalid soon. Here is a quote from it:
A hybrid Honda Accord costs about $3,800 more than the comparable non-hybrid version, including purchase, maintenance and insurance costs. Over five years, assuming 15,000 miles of driving per year, you'll make up that cost in gasoline money if the price of gas goes up immediately to $9.20 a gallon and averages that for the whole period.
This sounds like a math problem. Some of the questions that may be asked are "How much does a hybrid Honda Accord cost?" or "How many miles per gallon does the hybrid Honda Accord get? This is not a real type of question. It only exists because some people chose not to give some information. In this case, CNN chose not to state what the price of a Honda Accord was or how many miles per gallon it gets.
But what if we try to solve it? Let
H = cost of a hybrid Honda Accord
C = cost of a non-hybrid standard Honda Accord
The first statement then says:
H = C + 3800
The second statement assumes you will drive 15,000 miles per year over a 5-year period. That is 5 * 15,000 or 75,000 miles.
The third statement says that if it costs $9.20 a gallon for gasoline, then the costs of the two Hondas are the same. This seems somewhat more complex. Let the miles per gallon of the hybrid be h and let the miles per gallon of the standard car be c. Then the cost of fuel for the hybrid is:
75,000 miles / h miles per gallon * $9.20/gallon = $690,000/h
And for the non-hybrid:
75,000 miles/c miles per gallon = $690,000/c
The total cost of the hybrid is the purchase cost plus the fuel cost, or
H + $690,000/h = C + $3,800 + $690,000/h
And that for the standard car is:
C + $690,000/c
The story now states that these two are equal:
C + $3,800 + $690,000/h = C + $690,000/c
Or
$3,800 + $690,000/h = $690,000/c
This means we can't solve the problem for we have two unknowns in this equation and can't solve for either unless we know something more about these cars.
So now I leave these two problems as exercises:
1. Find c on the Internet; one way may be to Google for "Honda Accord 2005 mpg" or something like that. Then find h, H, and C.
2. Find h in terms of c and graph the result. What type of curve do you get?
A hybrid Honda Accord costs about $3,800 more than the comparable non-hybrid version, including purchase, maintenance and insurance costs. Over five years, assuming 15,000 miles of driving per year, you'll make up that cost in gasoline money if the price of gas goes up immediately to $9.20 a gallon and averages that for the whole period.
This sounds like a math problem. Some of the questions that may be asked are "How much does a hybrid Honda Accord cost?" or "How many miles per gallon does the hybrid Honda Accord get? This is not a real type of question. It only exists because some people chose not to give some information. In this case, CNN chose not to state what the price of a Honda Accord was or how many miles per gallon it gets.
But what if we try to solve it? Let
H = cost of a hybrid Honda Accord
C = cost of a non-hybrid standard Honda Accord
The first statement then says:
H = C + 3800
The second statement assumes you will drive 15,000 miles per year over a 5-year period. That is 5 * 15,000 or 75,000 miles.
The third statement says that if it costs $9.20 a gallon for gasoline, then the costs of the two Hondas are the same. This seems somewhat more complex. Let the miles per gallon of the hybrid be h and let the miles per gallon of the standard car be c. Then the cost of fuel for the hybrid is:
75,000 miles / h miles per gallon * $9.20/gallon = $690,000/h
And for the non-hybrid:
75,000 miles/c miles per gallon = $690,000/c
The total cost of the hybrid is the purchase cost plus the fuel cost, or
H + $690,000/h = C + $3,800 + $690,000/h
And that for the standard car is:
C + $690,000/c
The story now states that these two are equal:
C + $3,800 + $690,000/h = C + $690,000/c
Or
$3,800 + $690,000/h = $690,000/c
This means we can't solve the problem for we have two unknowns in this equation and can't solve for either unless we know something more about these cars.
So now I leave these two problems as exercises:
1. Find c on the Internet; one way may be to Google for "Honda Accord 2005 mpg" or something like that. Then find h, H, and C.
2. Find h in terms of c and graph the result. What type of curve do you get?
posted by Jim | 6:19 PM
3 Comments:
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