# Unit conversion problem

by cytochrome
Tags: conversion, unit
 P: 162 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?
 Emeritus Sci Advisor PF Gold P: 5,196 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.
 Sci Advisor HW Helper Thanks PF Gold P: 5,259 Another version: 6000 bbl per year per truck 1.9 x 1010 bbl per year
Emeritus