Question:
In a city of 100,000 people 50% of the population drive On average each driver goes 10,000 miles per year. The average fuel efficiency of the vehicles driven in the the town is 20 miles per gallon. How many gallons of gas are consumed by the people in this town during the year?
Ten years later the population of the town, the proportion of people driving, and the average number of miles driven per year all increased by 10%. What is the total increase and the percent increase in the number of gallons of gasoline consumed per year if fuel efficiency remains unchanged?
What change in fuel efficiency is needed to keep gasoline consumption constant?
Answer:
The total miles driven in the town is number of people x percent of people who drive x number of miles per driver. (100,000 x 0.5 x 10,000.) 500,000,000.
Divide total miles by fuel efficiency to get the number of gallons consumed (500,000,000/20) or 25,000,000 gallons.
Ten years later the population, the percent of the population that drives, and the miles per driver have risen by 10%. The new total miles driven is (110,000 x 0.55 x 11,000) or 665,500,000. Divide by 20 to get the number of gallons consumed (665,000,000/20) or 33,275,000.
This is a 33.1% increase in gas consumption between 2000 and 2010.
Fuel efficiency is amount of miles driven divided by gallons consumed. The fuel efficiency consistent with consuming only 25,000,000 million gallons (the 2000) level even though drivers in the town go 665,000,000 miles is (665,000,000/25,000,000) or 26.62 mpg.
This is a 33.1 percent increase in fuel efficiency.
Lesson from this problem is that without increases in fuel efficiency relatively modest increases in population, the proportion of the population that drives, and the average amount driven per year can lead to large increases in the amount of gasoline consumed.
Analysis in the problem is summarized below:
Year 
2000

2010

% Difference 
people 
100,000

110,000

10%

Percent drivers 
0.50

0.55

10%

Drivers 
50,000

60,500

21%

Miles per Driver 
10,000

11,000

10%

Total Miles 
500,000,000

665,500,000

33.1%

Efficiency 
20

20

0%

Gallons 
25,000,000

33,275,000

33.1%

People who enjoyed this post might also want to look at my post on issues related to carbon dioxide emission reduction that is achievable from a tax incentive.
http://dailymathproblem.blogspot.com/2013/04/carbondioxideemissionreductionfrom.html
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