Math – Applications for Living IV

I’ve seen the ads, often on the back of a semi-trailer, where companies say that they will pay so much per mile or so much per mile (and perhaps mention that drivers get to be home on weekends).  I can’t bring mathematics to the weekend issue for drivers, but I can  bring math to their pay system.

A typical rate of fuel consumption for the ‘big rigs’ is 8 miles per gallon (this is a little high, but is nicer for calculation!).   A truck’s speed is supposed to be 60 mi/hr in my state, and the average fuel price is $3.749 per gallon.  How much does fuel cost per hour?

    60 mi/hr * 1 gal/8 mi  * $3.749/gal  = $28.12  (rounded)

I have a problem like this on today’s test in my quantitative reasoning course (only it’s for a car, since not many of my students drive a semi).   If you are curious, a typical car would have  an hourly fuel cost of around $7 … we could get in to the cost per pound per hour, which adjusts for the much larger capacity of the semi for hauling stuff.  However, we can be sure that the average semi is loaded with far more than 4 times what a car carries.

Back to the start of this post … if a company pays semi drivers per hour, the driver has (normally) this fuel cost of roughly $30 per hour.  Now, when I see ads that say “$40 per hour to start”, I know that the real income is closer to $10 per hour.  If the pay is ‘per mile’, the calculation is a little simpler (1 gal/ 8 mi * $3.749/gal, which is something like $0.47 per mile).

Within our class, we are using problems like these to become more flexible in our proportional reasoning — a given rate can be represented in two fractions, with our choice being determined by looking at what we start from and what we need.
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