Unit conversion problem

cytochrome

1. The problem statement, all variables and given/known data
If one truck runs on 6000 barrels of oil per year, how many trucks could run on the oil produced in the US in one year (1.9*10^10 barrels)?


2. Relevant equations
(6000 barrels/year) used by one truck
(1.9*10^10 barrels/year) for US production


3. The attempt at a solution
I simply divided 1.9*10^10 by 6000 to get 3,000,000.

I'm confused about the fact that 3,000,000 is not in units of "trucks". How can I set up this problem properly to include trucks as my units?

cepheid

Hello cytochrome,

[tex]\left(\frac{1.9 \times 10^{10}~\textrm{barrels}}{1~\textrm{year}}\right) \cdot \left(\frac{1~\textrm{truck}}{6000~\textrm{barrels}}\right)[/tex]

The unit of barrels cancels, leaving trucks and years, so your result is in trucks/year ("trucks per year").

EDIT: ACTUALLY, you can consider the quantity of 6000 to have units of "barrels per truck, per year" which would be barrels/(trucks*years). So, in that case, there would be 1 year in the numerator of the righthand factor in parentheses, and the year unit would cancel as well, leaving only trucks.

However, the way I did it is fine too. In this case, the way to think about it is that a "truck" is a unit of volume equal to the amount of oil needed to run one truck for a year. So, what your unit conversion is doing is saying that the US produces 3,000,000 "trucks" worth of oil per year. It's just a matter of interpretation.

Chestermiller

Another version:

6000 bbl per year per truck

1.9 x 10¹⁰ bbl per year

cepheid

Yup. I had edited my post to include this version (just not LaTeXed).