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PHYS171_f11_lecture_supp_02 - improves to 0.05 gallons/mile...

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PHYS171 Fall 2011 Prof. La Porta Fuel Economy Question: An SUV owner drives 10 miles to campus, getting 10 miles/gallon. A Honda Civic owner drives the same distance, getting 40 miles/gallon. Assume that each driver replaces his or her vehicle with a hybrid model which gets twice as many miles per gallon. (the hybrid SUV gets 20 miles/gallon and the hybrid civic gets 80 miles/gallon) Question: who saves more gas by making the switch? It sounds like an improvement from 40 to 80 miles per gallon is more impressive than an improvement from 10 to 20 miles per gallon. But when we talk about an improvement in miles per gallon we are describing how many extra miles you can go on a fixed amount of gas. That is not the right question to consider. The relevant question is how much less gas is used for the same number of miles. We should therefore express fuel economy in gallons per mile. This is obtained by taking the inverse of the milage. The SUV then consumes 0.1 gallons/mile, which
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Unformatted text preview: improves to 0.05 gallons/mile. The Civic gets 0.025 gallons/mile, which improves to 0.0125 gallons/mile. Fuel Consumption Summary The result is that the SUV owner saves more gas by upgrading than the Civic owner. Both drivers use half as much fuel as before, but since the Civic is using so little to begin with, the amount saved is small compared with what the SUV owner saves. (Of course, the most dramatic savings would occur if the SUV owner switched to fuel efficient vehicle.) SUV ( ) ( ) gal. 0.5 is savings gal 5 . mile 10 mile gal 05 . : hybrid gal . 1 mile 10 mile gal 10 . : al convention = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Civic ( ) ( ) gal. 0.125 is savings gal 125 . mile 10 mile gal 0125 . : hybrid gal 250 . mile 10 mile gal 0250 . : al convention = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛...
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