Estimate the number of gallons of gasoline consumed by the total of all automobile drivers in the U.S., per year. Suppose that there are about 3 × 10^8 people in the United States, approximately half of the them have cars, each car drives an average of 12,000 mi per year, and consumes a gallon of gasoline for each 20 mi?
3 x 108 is roughly 300 people.
Half of them have cars. Half of 300 = 150.
150 x 12000 = 1,800,000 miles driven.
Each car gets 20mpg.
Solve for the # of gallons consumed.
Answer:
\(G = 9 \times 10^{10} gallons\)
Explanation:
Total number of people in US is \(N_p = 3 \times 10^8\)
Only half of them have cars. So, Number of cars in US
\(N_C = \frac{N_p}{2} \\\\N_C = \frac{3 \times 10^8}{2} \\\\N_C = 1.5 \times 10^8\)
Each cars drives 12000 miles, so total distance travelled by all of these cars combined
\(D = N_C \times 12000\\\\D = 1.5 \times 10^8 \times 12000\\\\D = 1.8 \times 10^{12} miles\)
To travel 20 miles, we need 1 gallon of gasoline
Amount of gasoline required to travel one mile is \(\frac{1}{20}\) gallons
Amount of gasoline required to cover the distance 'D'.
\(G = D \times \frac{1}{20} \\\\G = 1.8 \times 10^{12} \times \frac{1}{20} \\\\G = 9 \times 10^{10} gallons\)
Amount of gasoline required to cover the distance 'D'.
\(G = D \times \frac{1}{20} \\\\G = 1.8 \times 10^{12} \times \frac{1}{20} \\\\G = 9 \times 10^{10} gallons\)