So far we've only done problems that start with a single unit, and end with a single unit. But thingscan get more complicated than that. For example, how would you convert miles per hour into feet per second?

First, you need to understand how to write miles per hour and feet per second in mathematical notation:

miles per hour = miles/hour
feet per second = feet/second

These units are fractions. When you see per, it means that the unit following will be the unit in the denominator.

Example One - Convert 60 miles per hour into feet per second.

This problem has two units (miles and hours) that we don't want to have in our answer, so there's a pretty good chance we're going to need to daisy chain conversion factors together to get our answer. Let's start with the easy part:

(60 miles/hour) x (5280 feet)/(1 mile) = 316,800 feet/hour

Well, that's nice, but it's not what we want - we want feet per second! But notice that the unit we now want to get rid (hours) of is in the denominator. So to get it to cancel, we need to put it in the numerator of a conversion factor:

(316,800 feet/hour) x (1 hour)/(60 minutes) = 5280 feet/minute.

Again, not quite what we want - we don't want minutes, we want seconds! So we do one more multiplication:

(5280 feet/minute) x (1 minute)/(60 seconds) = 88 feet/second.

Of course, we could have done this all in one line:

(60 mi/hr) x (5280 ft)/(1 mi) x (1 hr)/(60 min) x (1 min)/(60 s)

Example Two - Convert 10 miles per day into feet per hour.

Answer - The conversion factors we need are (5280 feet)/(1 mile) and (1 day)/(24 hours).

(10 mi/day) x (5280 ft)/(1 mi) x (1 day)/(24 hr) = 2,200 ft/hr.