Unit conversion problem

Homework Statement

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)?

Homework Equations

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

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?

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cepheid
Staff Emeritus
Gold Member
Hello cytochrome,

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

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.

Last edited:
Chestermiller
Mentor
Another version:

6000 bbl per year per truck

1.9 x 1010 bbl per year

cepheid
Staff Emeritus