Monday, December 30, 2013

Gas consumption and growth in a hypothetical town.

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/carbon-dioxide-emission-reduction-from.html

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