### Rough Estimates

Sample problem 1: How many gallons of gasoline are used for cars, trucks, and SUV's every year in this country?

By making a few assumptions we can come up with a reasonable estimate. This is known as a "back-of-the-envelope" calculation.

Assume the population of the US is 300 million, with one vehicle for every two people - therefore 150 million cars.

Assume that each year the average vehicle covers, 15000 miles and gets 20 miles per gallon. This requires 15000/20 = 750 gallons.

The total is 150 million cars x 750 gallons/car = 112.5 billion gallons. We round off to 100 billion (1 x 1011) gallons, since we're just looking for an order of magnitude.

Sample problem 2: How many street lights should be out on my bike ride home?

For my 5-mile trip, assume 40 lights/mile. This gives 200 lights on the trip.

Lightbulb lifetime 3 years (~1000 days). This implies that 0.2 lights should burn out daily along my route, or 6 lights burn out per month.

Assume that there there is one light-bulb repair truck in Brookline that changes 10 light bulbs and covers 10 miles per shift, or 200 miles per month.

Town of Brookline is approximately 25 square miles. Assume one-half the area is urban. Assume a grid road geometry with all roads of length 5 miles that are separated by 100 yards. Total road length is approximately 400 miles. So one repair truck should cover the entire town in 2 months.

So there should be 12 lights out on my bike ride home if there is 1 repair truck is dedicated to replacing street lights.