## Ask Professor Puzzler

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Kobe from Mephis asks, "What conversions are used to convert miles per hour to miles per minute?"

Well, Kobe, unit conversion is a very important topic to understand, so rather than just giving you a quick answer to your question, I'm going to show you how to go about figuring it for yourself, okay?

Let's suppose you have the quantity 60 ^{mi}/_{hr}, and you want to convert it to ^{mi}/_{min}.

In order to do this conversion, you're going to have to multiply 60 ^{mi}/_{hr} by one or more conversion factors. What is a conversion factor? Well, I like to tell my students that a conversion factor is just *one*. After all, if we're going to multiply 60 ^{mi}/_{hr} by something without changing its value, that "something" has to be the number 1. It might not *look* like the number one, but it has to be equal to 1.

So let me ask you a question: How many minutes are there in an hour? Hopefully you said "60."

So 1 hr = 60 min, right? But if 1 hr = 60 min, then ^{1 hr}/_{60 min} must be equal to one, because the numerator and the denominator are both equal to the same thing. This is a conversion factor. Of course, ^{60 min}/_{1 hr} is also a conversion factor, right? We're going to use one or the other of those two conversion factors; we just have to figure out which one. So we write out an equation:

60 ^{mi}/_{hr}× _____ = ? ^{mi}/_{min}.

The big question is, what is the conversion factor I'm going to put in that blank space? Well, I'm going to choose the conversion factor that causes the unit "hours" to disappear from the equation. After all, I don't want to have "hours" in my answer, right?

So I look first at where the "hours" unit is in my equation. It's in the *denominator* of the units. That means I want to use the conversion factor that has "hours" in the numerator. Why? Because if there's "hours" in the denominator, and "hours" in the numerator, they'll cancel each other out, which is what I want!

So we do this:

60 ^{mi}/_{hr}× ^{1 hr}/_{60 min} = ? ^{mi}/_{min}.

Now we multiply across. Notice that our conversion factor doesn't just get rid of the "hours" unit - it introduces the "minutes" unit into the denominator - which is great - that's the unit we want in the denominator. When we multiply across, the "hours" cancel, and since we have a 60 in the numerator and a 60 in the denominator, they cancel as well, leaving us with:

60 ^{mi}/_{hr}× ^{1 hr}/_{60 min} = 1 ^{mi}/_{min}.

And that's it, you're done! We can get more complicated than this, because sometimes you'll run into conversion problems which require you to convert *two units*. For example, converting miles per hour into feet per second! For this one, you'd need to convert miles to feet *and *you'd need to convert miles to seconds. So you'll have two unit conversion factors in order to solve the problem.

Thanks for asking!

Professor Puzzler