You are here:

# Advanced Math/Per Hour, Mile, Etc.

Question
QUESTION: Hello:

Is it incorrect to use the word "per" with rates in which the denominator is more that one or 1?

Example: It is common to hear, say, or write, 50 miles per hour, indicating 50 miles per one hour. Is it incorrect to say or write 150 miles per 3 hours?

This question may be more of an English usage question that mathematical.

ANSWER: Yes it is, it's just that most of the time people only put a 1 in the denominator.
For example, 50 miles per hour is the same as 2000 miles per 40 hours since 2000 = 40*50.

It is usually put as mph, but to write it out mathematically,  that is the really 50 m/h.
If conversion to other units are desired, just multiply so the units cancel.
For example, to compute miles/day, we would need to multiply by 24 hours/day.
That is really (24 hours) / (1 day), or (24h)/(1d).  The bottom is usually 1,
so the number is not put in.  Note that 24h/d is 48h/2d, or 12h/0.5d,
but 24 is used since there is a 1 in the denominator).

In manufacturing businesses, most people tend to ignore whether the units are on the top or bottom, but should really pay attention to it.  For example, I have seen a job where something was measured in inch-pounds.  I then saw the conversion to foot-pounds was to multiply it by 12.
This means the measurement is really in pounds/inch since it was multiplied by 12 inches/foot.
When this is done, the new units have inches/inch, and that cancels.

We found it very important in physics, chemistry, biology,
or any other science to always cancel the units.

---------- FOLLOW-UP ----------

QUESTION: Hello:

I'm somewhat confused.  Are you indicting that it is okay or not okay? I asked whether or not it is "incorrect" and you indicated: "Yes it is, ..." Does this mean yes it is incorrect or correct to use the word "per" with rates in which the denominator is more than 1?

I thank you for your clarification.

Every time people say, 'per,' it refers to a coefficient of 1 in the bottom of the fraction.
It might be per gallon, per pound, per foot, per second, per minute, per hour, per ton, per liter, per foot, per mile, ... the list goes on.  In each of these, it is assumed the speaker is talking about a unit of 1 gallon, 1 pound, 1 foot, 1 second, 1 minute, 1 hour, 1 ton, 1 liter, 1 foot, 1 mile, ... or whatever else.

If, 'per,' is used with anything besides one, the number must be given.
For example, bananas might be \$1 per 2 bananas, which implies 50c per banana.

If the price of widgets was 20c each, it could be said they had the price of \$1 per 5 widgets.
It could also be said that they were selling at \$2 per 10 widgets, or \$10 per 50 widgets.
Note that when the bottom does not have a 1, the number must be stated.
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks for the great clarification reply!

Volunteer

#### Scott A Wilson

##### Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

##### Experience

Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.