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O/T-impossible math question

C

cornfarmer

Member
OK, I admit it-my math skills need help.If a car gets 25 mpg in the city, and 40 mpg highway, what is the average if driven for 10 miles in the city and 50 miles in the country. Problem is, I come up with two different answers depending on my method.
Method 1-weighted average-since 50 is a multiple of 10, I should be able to add 25+40+40+40+40+40=225. Then take 225/6=37.5 mpg.
Method 2-fuel consumed. The car uses .4 gallons of gas to go 10 miles at 25mpg, and 1.25 gallons of gas to go 50 miles at 40mpg. So, 1.25+.4=1.65 gallons used. 60 miles divided by 1.65 gallons used=36.36mpg.
Question is, which one is correct?
 
25 mpg city @ 10 miles
40 mpg hwy @ 50 miles

If (in the city) one gallon = 25 miles
Then 1/25 gallon = 1 mile
You drove 10 miles in the city
so 10 miles times 1/25 gallon = 10/25 gallon = 2/5 gallon

And similarly,
On the highway one gallon = 40 miles
so 1/40 gallon = 1 mile
You drove 50 miles on the highway
so 50 miles times 1/40 gallon = 50/40 gallon = 5/4 gallon

For the total trip you used 2/5 +5/4 gallons
= 8/20 + 25/20 = 33/20 gallons
And you drove a total of 60 miles.

So 60 miles per 33/20 gallons is the average.
or
60/(33/20) = (60/1)/(33/20) = 60/1 * 20/33
= 1200/33 = 400/11 miles per gallon
or
36.363636 miles per gallon average

Pooh Bear
 
This is a classic example of something that looks like it is good math, but isn't. Your average mileage is simply (total miles driven)/(total fuel consumed). Your first formula doesn't give you that.
 
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